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: 
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).
To add to all the great answers given;

* It can be very cold in the airplane, I like to take a pair of warm socks with me.
* The air can be very dry and rough on the skin, I prefer to take a moisturising cream and lipbalm with me, so I don't start my holiday with itchy, cracked skin and lips.