Most Crucial Gear/ Accessories for a (Road) Cycling Beginner? Some background information on myself before I get to the question:

I've decided to get in to cycling both as a hobby and because I need the activity. (Though I'm honestly driven more by the former - I've always enjoyed riding since I was a kid.) I already have a bike that seems decent to me (for someone in my position), but I'm also a newcomer and don't know that much. It's a 2004 Cannondale R800. When I was about 15, my dad and I each got one to start together. Long story short, we had some demotivating initial experiences with the clipless pedals, moved shortly after, and soon the bikes were (sadly) forgotten.

Now (~6 years later), I'm looking to actually get into it, and it seems that there is a lot of "essential" gear I should buy. I have somewhat limited funds (as a student), and can't do it all at once, so was hoping for some guidance in both what I absolutely need to get, and what would be more ancillary. Also, recommendations on around how much I should be spending on different items would be helpful. For example, I know headlights can run anywhere from $10-$1000+, but I don't know what the sweet spots between performance and value are.

I live in a fairly rural environment in a university town of ~21k people. There is a decent bike shop in town considering the size, however their focus is much more casual/ kid-oriented.

What I do have:

Jersey (longsleeve + shortsleeve)
Cycling Shorts
Cycling Shoes
Helmet
(Small) Saddle Bag
Pump
Emergency Patch Kit


Things I don't have, but are on my radar to acquire (at some point):

Headlights / Taillights
Cycling computer / heart monitor (I do have an Android phone that I know can facilitate this point.)
Additional clothing, though nothing particular at the moment
Gloves
Tool kit


I'd like to be fairly serious about it, though training for self-improvement, not competition. I'm planning to gear up to riding my first century this September.

Tell me if there's any more information I need to add, and, thanks!
Sounds like you have the basics covered pretty well.... If you're turning in some serious mileage, you want to be able to handle flats and minor repairs on the road.
Minimum is a good frame pump ( a lot of the mini pumps have trouble getting past 50 pounds or so...) spare tube, tire tools, etc.  Some of the handy little hand-cleaning wipes are a good idea as well.
A multi-tool that will take care of most emergencies is a good investment; it should include a chain breaker, allen wrenches to fit the fasteners on your bike, etc.
Some money is never a bad idea.  You may just HAVE to have a donut....