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I would say that the female characters are supposed to make bad decisions despite being good people. 
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Emily:
She really cares about appearances. She has her interests and her life and her daughter constantly tries to undermine that. She finds dignity in her world and seeks that but her daughter constantly challenges that. When push comes to shove, she typically does the right thing or she will surprise you by always wanting what's best for Rory despite her being an asshole about it up to that point.
Lorelai:
The point you made about Lorelai with Rory and Yale/the financial aide is valid. I think it was poor writing to create a new conflict for the plot. Lorelai up until that point is very consistent with Rory. Everything in her life is sacrificed to protect Rory from the life she ran away from. That conflict kind of ruined the character for me. Before that she was an amazing mother who sacrificed everything for Rory. That story arc ruins that for me. She becomes an immature teenager who never grew up after that.
With Max, Lorelai saw too much of a connection to her mom's world. Luke represents the life she found which is ultimately the life she wants. She can also see that her relationship with Max is effecting Rory which was the entire thing she was avoiding for Rory's whole life up until that point. Luke was always consistent in his care for Rory and ultimately he was the person she wanted but she didn't want to admit it to herself because she thought she was supposed to be with Christopher. 
Lorelai's main arc is realizing that she was only seeing what she wanted to see with Christopher. That he was always the same person and that they would never work. She does a ton of damage to people get to that point. I don't think the show wants her to be a hero. Just a flawed person who is ultimately a great mom and is extremely competent while doing things her own way.
Rory:  
This was the thing I disagreed with the most. Rory is a young woman. She has zero good role model in relationships but very good role models in her life for most other things. She has to learn the hard way with relationships and she gets no help. With Dean she leaves him for Jess replicating the same mistakes her mom would make. Nobody in her life likes it for her. Ultimately she is saved by Jess' flaws. She tries to recreate what she had with Dean but it's obviously too late. She gets with Logan who was also never good for her despite him overall having good intentions.
Overall, I think Rory has the most realistic and well written story arc. I think Emily is an amazing antagonist and I wish the show went deeper into her background. I really like Lorelai except for a few decisions which I thought just didn't fit her character.
About Emily...

It was Richard's hard work that built the beautiful house he and her lived in, and when they separated, she had the nerve to make Richard live in the pool house.

Leading up to their separation, the show made a subtle point that Emily, like a lot of spouses of her time, contributed quite a lot to Richard's success in the form of managing his social calendar, (building social capital) decorating their home and maintaining his wardrobe (signaling their status to their peers) and doing all the other (unpaid, and often unvalued) domestic work to allow Richard to focus on his work. And while Richard did benefit from those things, he was completely oblivious to them, and thus felt no appreciation or gratitude towards Emily for her labor. 
You can argue she's not a good person, but 'immature' seems a poor fit. >

She’s a shrew. That’s why I always jokingly call her Katherine. >

Sure... but even in Taming of the Shrew, Kate isn't immature. And she isn't wrong about being treated like a piece of property instead of a person. She's a shrew because she's smart enough to realize she's getting the bad side of the deal, and confident enough to speak up about it. >

The main point of the show is that Lorelai was and is a child acting above her capability to make the best for her daughter, and Rory was and is a child acting above her capability for her mother.
Lorelai was controlled and manipulated as a child. The consequence of that was that she became pregnant and was left in the situation where she didn't have the opportunity to develop balance and control that comes with adulthood. 
Similarly Rory wasnt allowed to experience learning how to be an adult because she had to act like an adult when she was a child. 
So, yes, they are immature in some sense, but also overly mature in others. The point of the show is that generational harm is very difficult, even when people have good intentions. 
But further, you are missing the key parts of the characters maturity. Lorelai goes back to her mother for the benefit of her child. It is reluctant, and with some difficulty, but she does believe she can sacrifice to make her child's life better. 
Of course, again the show poses a question: is that the right choice? We can see the harm that Lorelei's mother does to Rory.
Then they grow and mature through the course of the show. Lorelai becomes more stable, Rory is permitted to make mistakes and recover from them.
As to whether they are good people: Lorelai and Rory love each other and make sacrifices for each other throughout the show. They are flawed, but not bad. >


The main point of the show is that Lorelai was and is a child acting above her capability to make the best for her daughter, and Rory was and is a child acting above her capability for her mother.

I would say it is more her trying to do things her own way without a model on how to do things a way different from her parents. Her bad decisions are her figuring things how as she goes. Making mistakes and then having to repair them in her own way.
Her main conflict in the show is rejecting all of the ways of her mother while always wanting to do the right thing for Rory. There are times >

Lorelai flits between Christopher, Luke, and Max all the time. She is codependent on Rory which is weird. 
Emily is a see you next Tuesday but I kinda like it. 
Babette and Sooki are the best female characters in terms of role models. 
I just love that show. Taylor is one of my favourites.
Does anyone have any suggestions for shows similar to GG? >

I love Taylor as a character because I find him so infuriating. He is a suburban fascist. 
In a different time and place he would have been ratting out enemies of the state. >

Suburban fascist..  Hahaha! He's just a male Karen who is power mad. >

... that's where fascists come from, it's just that most never get the opportunity to flex that power except over little suburban issues. >

Haha, yeah I agree. >

Emily, Lorelai and Rory are undoubtedly flawed people. They're obnoxious, childish, manipulative, co-dependent, and shockingly self centered. They're often cruel, and have all done unquestionably immoral things. There's merit to the view that the three of them are the villains of the show.
I think the situation is more complicated than that though. Lorelai and Rory both live in what is essentially a cult. It's an isolated community in which almost everyone worships them, or at least - worships a very specific view point of who they're supposed to be. Compliance with this view point is met with constant reinforcement. Emily also lives in a restrictive world with very rigid rules and expectations.
The narrative arc of the show is that all three of them struggle with this situation. They're not sure whether or not they're the people that their environment claims that they are. They're not sure if it's okay not to be. They're not sure who they can be if they're not. They desperately try to find some version of themselves that makes sense in other people. They struggle and almost always fail. They don't meet their own expectations or the expectations of others. In the end they sometimes learn.
If you judge them by the standards that everyone around them holds them up to, they fall far short. For instance, Rory is not a humble and modest prodigy whose writing is going to change the world. If you view them as people who try to be good in face of unhealthy upbringings and living conditions, and are willing to be somewhat understanding of the times when they fail, then they're not as awful as you may think. >


It was Richard's hard work that built the beautiful house he and her lived in, and when they separated, she had the nerve to make Richard live in the pool house. 

Richard's career involved a lot of business dinners and networking opportunities that Emily organized for him and participated in. She also took care of all of the other aspects of their home, including decor and upkeep. 
To say it was just Richard's work or that he deserved the home more than Emily did seriously devalues the work homemakers do. 
Ultimately, of course, all of these characters are flawed. But all people are and perfect characters are boring to watch. >


She makes her decisions based on if it's going to piss her mommy off, or to spite her mother.

She specifically doesn't. She might complain and be upset, but she agrees to allow her parents back into her life on a regular basis to help her daughter
She's definitely immature at times, but saying she makes her decisions on spiting her mother is inaccurate. If she did, she wouldn't have agreed to Friday night dinners at all >

Lorelei just wants her narcassistic and controlling (read: abusive!) mother out of her life. She takes no joy whatsoever in playing games with Emily. She thought putting Rory first meant swallowing her pride and asking her parents for a loan to pay her tuition. She wouldn't spend any time around Emily if Emily didn't make it a condition of the loan,  and besides her contractual obligation to attend dinner on Friday nights, she tries to minimize involvement with her mother as much as possible. 
Lorelei valiantly tries to keep it together around Emily, but that's hard to do perfectly when Emily would frequently spend the entire dinner demeaning her, picking at her insecurities, even ignoring her existence. Emily also tries to meddle with how she raises Rory, thinking she knows best, and ultimately she does deliberately and methodically tempt Rory into a lifestyle of privilege, something Lorelei never wanted for her.
See the following conversation from Season 1, Episode 18, wherein Lorelei and Rory gets a sudden windfall (easily enough to pay back their loan) and Emily tries to prevent her from taking it:

EMILY: “You know as well as I do that money is freedom. […] Why should she wait to backpack around Europe with you? She could afford to go herself. And she could take a friend or a boyfriend or anyone.”
LORELEI: “Yeah, well, she wants to go with me.”
EMILY: “Well now, of course she does, she doesn't have options. But the minute you give her options…”

Emily was the one who was supposed to dangle tantalizing “options” in front of Rory, to tempt her with their access and lifestyle and ultimately gain more direct influence over her. She's jealous of Lorelei and Rory's relationship, and wants Rory to be the "perfect" daughter she never had. The only one that stands in her way is Lorelei and her shrewdness to how Emily plays games. 
(Ultimately Emily sort of succeeds - once Rory sees how far a little privilege will go, how the name "Gilmore" can open doors, she's sold. As an adult, she willingly enters her grandparent's orbit and unsurprisingly starts making more selfish and self-deluded choices as a result.)

EMILY: “It's terrible not to be needed. You'll see!”

It's pretty fucked, and I think Lorelei gets a gold star for how she deals with Emily.
Lorelei is in general a logical descion-maker, a responsible and loving mom, a business-owner and event organizer, and a contributing member of the Stars Hallow community in so many ways. I don't know where people get this idea that she's some stunted woman-baby. She likes childish humor, she certainly has flaws, but nevertheless she's a grown up who for the most part has her shit together. >

I'm not disagreeing with your character analysis, but I always assumed they were meant to be perceived this way. ETA, I thought the writers intentionally made them look shiny (pretty and bubbly and successful) on the surface, but flawed once you dig in a little. >

I thought this said golden girls because we were about to fucking fight >

If someone did slander Blanche Dorothy Rose and Sophia you bet there’s be a row and I’ll be on your side >

This reminds me of a time back in Saint Olaf… >


It was Richard's hard work that built the beautiful house he and her lived in, and when they separated, she had the nerve to make Richard live in the pool house.

Got it, married people are not equal partners. Cool. >

Logan cheated on Rory and I don't care that he thought they were "broken up" because he should of made sure. He could of asked or even just waited longer to find out for sure. Also I dislike his family for the way they treat people who are not as rich. >

They aren't real people. TV shows need conflict to function. They are dialed up versions of real archetypes in families that people can relate to, but just absurd enough that you can laugh at them. You can't judge fake people that were invented to have problems by writers. >

Lorelei is an underaged mom who puts several elements of her life on hold, rekindles a weekly interaction with her own mother that she DREADS for the sake of providing Rory a better opportunity, seeks stability in relationships without ever letting them interfere or destabilize Rory's life, is a beloved friend around town to most people, and also runs a successful entrepreneurial enterprise. Compare that to the 32 year olds you know, let alone the ones who had kids at 16. She maintains a cordial relationship with Christopher and even when he's absent she doesn't influence Rory to turn against him. And while she is more friend than mom to her daughter, somewhat out of necessity, shows ethics and morality and stern rebuke to some of Rory's worse moments like hooking up with a married Dean.
So she's a bit flighty and crass and has an imperfect relationship with her mom. Totally small potatoes in the grand scheme.