Edit: I guess there are unlockables for your PSN Home as well. They may or may not be the same as the ones for the 360.
Anyway, here is a working list of Avatar awards and the way to get them. I will update the post as I discover more! Please post if you find any! I will post pictures of my avatar wearing the different clothes when I get the chance.
Shoot somebody’s hat off.
Complete a Community Challenge
"Red Dead Redemption is available in stores now but the fun doesn't stop after you play through the main story and conquer multiplayer. A series of Rockstar Challenges are COMING SOON. By completing these Challenges together as a community, you can all earn some truly excellent rewards. The first Rockstar Challenge will be "Strike it Rich", which when completed will grant every community member the Posse T-Shirt."
Source [ https://socialclub.rockstargames.com/games/...Fcommunity.html ]
Yellow Rockstar Logo T-Shirt
Black on Red RDR Logo T-Shirt
It's in a chest at the burnt out cabin in Riley's Charge, which is just SSW of Armadillo and just E of Rio Bravo.