Hello, and welcome to the wonderful world of Shadowrun! We're thrilled to have you!
The important part is to pick up the SR4 core rulebook. Once you've done that, technically, you're done!
There are plenty of other books that you can pick up, but none of them are absolute must-haves. The Runner's Toolkit (An Origins Award winner, now) is probably the top item to get, otherwise. Austin has a few gamestores, I'd wager, being something of a college-friendly town, so I'd certainly sniff around and see if there're any local groups. If not, starting one makes you a hero.
(As an aside, always try to shop your local stores first, Amazon and other online retailers second. Books are cheaper online, but locally, you can make a difference for a store owner and, in addition, your regularly asking for books from a line encourages them to stock more. More books stocked indicate a popular item, and if you talk about it some while their, you can get other people stoked as well. Who knows? You could be the one that starts a Shadowrunning regular group there!)
The Expansion Books, with lots of Stuff in them, are:
Arsenal, about guns, swords, guns, chemicals, guns, vehicles, and, oh yeah! Guns.
Augmentation, about new cybertech, bioware, nano-tech, and genetic upgrades.
Street Magic, about magical stuff.
Unwired, about hacking and computer stuff.
Arsenal's the one that EVERYBODY can use, so I personally slot it the highest of the four.
After that, you have a bunch of adventures all written up for you, 'fluff' books that detail the world of Shadowrun, the people to see, the places to go, and the things to do. Attitude's a nice one of the recent crop for that, while Seattle 2072 will walk you through the main setting.
There's gobs more, but, go slow, chew what you eat, and when you're ready for seconds, we'll be here for you.
Stay frosty, chummer!