The I3 has the most performance until you hit multithreaded apps (very few games) or do multitasking. The I3 on a lga1155 board has the best CPU upgrade path, funds allowing an upgrade at a later date.
I would always choose an Intel product; however, since you are on a budget, I would go with the 965. You can overclock it safely to 3.8 and sometimes 3.9 Ghz.
This would be my choice, but ONLY if I never planned to upgrade the processor. Like amuffin said, you can always upgrade with the 1155 socket. Plus the core prices will likely drop when Ivy Bridge releases.