I have an AT&T Galaxy S3 and cracked my screen back in May. Here's what I purchased:
Replacing the glass wasn't difficult for me (but it has been for others)- you just have to read all the instructions you can find. Watching a tutorial on YouTube is helpful as well. The instructions it comes with are pretty bad; follow the ones on iFixIt and this helpful Amazon review.
If you want your glass repair to look OEM, then I HIGHLY recommend using the LOCA glue. What this does is it adheres the glass to the digitizer and allows accurate touch points. It also fills the gap between those 2 components which some people didn't understand that a direct glass replacement isn't enough. Watch this LOCA glue replacement on YouTube for a better understanding. The glue I purchased is currently sold out, but anything similar will do just fine.
Tips: