The 965BE isn't a bad budget gaming Cpu, it's just harder to find. So the fx6300 took it's place as the go to budget gaming Cpu. Both chips overclock well, and offer similar performance in games. Generally the 965 was about 25 dollars cheaper though which made it a better buy.
I'd buy a socket AM3+ motherboard, the 965 BE Cpu and a Hyper 212 Evo. You can generally overclock that Cpu to 4ghz or so, and you'd have a heck of a performer for the money spent. Like I said earlier, later on if you feel the need you can toss in the latest AM3+ 8-core Cpu(the last I heard was that the next-gen cpu's from AMD were going to be socket AM3+) and you'll be just fine for several years at least.