Welcome to brewing! Personally I do 5 gallon brews and started with full boil extract beers. If this is also where you are starting there are any number of things that you would need.
-Boil kettle (a 30qt aluminum kettle and propane burner are great if you can brew outside or in a garage. It is cheap and works well for many people, including myself). If you brew inside, you will probably want a smaller kettle, something that can fit on your stove, and you will likely be doing partial boils, which I know a number of people do).
Then the kits. I personally got mine from midwestsupplies on a groupon thing. Works well for me. http://www.midwestsupplies.com/brewing-basics-equipment-kit.html
I'm sure there are other sorts of kits similar at you LHBS or at austin homebrew supply, williams brewing, northern brewer or other spots, but that's just where I got mine at, all serve the same purpose!
That is pretty much all you need to start with.....
If I were to start all over again, I would add in a couple of things on top of those:
-Starsan (get at least a 16oz bottle, it wont really go bad and it's amazing!)
-autosiphon (if you dont have one in the kit that you pick it's worth the money)
-glass carboy (or any type of carboy[google: glass vs plastic carboy for the full story], you will get to a point where you want to age beer for longer or have more beers going at once if you are anything like me, and its very useful.)
http://www.midwestsupplies.com/brewing-starter-kit.html <-this is what I would do if I were starting over again, and pick up the star san on the side.
If you want to go all out and do All grain.... well then that's a whole different boat, but all the above equipment + more things would be needed.