Question: I am traveling from the US to Australia. What type of under the seat bag is practical, and what should be stored in it for the flight?

Answer: 
The following is a list of the sort of items you should include in your cabin luggage (eg. not your checked luggage):

* All valuables (jewelry, money, etc)
* Important documents (passport, itinerary, hotel reservations, medical prescriptions, etc)
* All electronics (phone, laptop, mp3 players, etc)
* Anything fragile or which might break due to rough or careless handling
* Medication, especially any that you may need to take during the flight such as lactose pills, air sickness pills, pain relief for headaches, etc.
* Anything you may want to use during the flight

What goes under the seat should be the stuff you intend to use during the flight. This may include: some electronics, like a laptop or iPod; a travel pillow; books or other reading material; a blanket or jacket; essential toiletries (eg feminine hygiene products), and so on. 

It's a matter of preference, of course, what you do on the flight. But if you think you'll want to listen to your iPod, it should go under the seat rather than in the overhead so you're not needing to go rummaging. (Going into the overhead on an overnight flight is especially difficult since the crew tends to dim or turn off the cabin lights, so you'll be doing said rummaging in the dark.)

What type of bag you use depends on what needs to go into it. If you're just taking your passport and an iPod and planning to nap most of the trip, you can get away with using a purse. If you're taking more, a backpack may be more practical. The type of bag also depends on what you're actually planning on using in your destination, since taking excessive luggage just for the plane trip isn't always practical.

But in general, the bag should be soft so that it can be fit under the seat and potentially squished a bit. It shouldn't be excessively large in any dimension -- check with your airline for dimensions. And it should be relatively easy to get stuff in or out of it. (Eg a zipper rather than a system of six buckles.)
A few bonus tips to go with [Roddy of the Frozen Peas](https://travel.stackexchange.com/a/67602/16725) excellent answer:

* Don't make the bag too big, as it will be taking up some of your legroom. Some aircraft have electronics boxes for the in-flight entertainment system under the seat, which further reduces the available space. You can always put it in the overheard if there's space, particularly if you have an aisle seat. With a window or middle seat, I'll usually pull the items I need out of my bag before sitting down and put the bag in the overhead, space permitting, but that's up to you.
* Make sure to bring any chargers for your electronics. There may be outlets available at your seat.
* Try to designate a particular place in your bag for your travel documents (passport, boarding pass, etc...) so you can find them easily when you need to. Going along with that, don't forget your passport is in your bag if you've zipped it into a special compartment.
* For long flights, especially overnight ones, consider bringing some basic toiletries to freshen up before arrival. This may involve a comb, razor, toothbrush, etc...
* Remember that your checked luggage could be delayed or even lost, or you may experience flight delays that leave you without access to your bags for an extended time. Carry with you anything that you must have upon your arrival or at your destination, even if you won't need it on board the plane. This is especially true if your itinerary might involve a close connection or multiple changes of planes, as there's a higher chance of being separated from your bags under such circumstances.
* If I'm checking the majority of my luggage and just bringing a small personal bag on board, I usually like to carry at least some emergency clothes in my carry-on in case my luggage gets lost. Being separated from your luggage is never fun, but it's a little better if you have a clean shirt and a pair of underwear ready for that eventuality. If you're giving an important business presentation and absolutely must wear a suit, don't pack your only suit in your checked luggage. (To those Italians at that New Year's gala where I showed up in baggy jeans and a not particularly clean t-shirt and you all assumed I'm an ignorant American who can't dress himself: I am, once again, sorry.)
* I like to bring an extra tote bag that folds up really tight ([like this](http://baggu.com/collections/category-travel/products/7-02382-68458-7?variant=6936184065), only hopefully for far less than $64). Takes up minimal space going, but gives you room for purchases and extra stuff on the way home.
* Many countries (particularly the US and much of Europe) have restrictions on the quantities of liquids allowed in carry-on (not checked) baggage. If you're traveling through a location with such restrictions, don't carry more than the allotted limit. There should be an exception for medically necessary liquids.
* Even if your flight includes meal service, you may consider bringing some snacks along, especially if you often get hungry or are picky about food. For international flights, be sure to either dispose of any leftover food before going through immigration and customs, or declare it to the proper authorities upon arrival. (Australia is particularly strict about importing food. If you declare all food and show it to the inspectors, there shouldn't any any problem and they'll let you know what is allowed in, but you can be fined for trying to bring in food without declaring it).