For gaming, go with a Phenom II X4 9xx (like 945) and a 785G chipset motherboard.
Core i3 540 is also a good choice, if you want to go Intel. No real advantage to that though, other than lower power consumption. The motherboard will be a bit more expensive.
AMD vs Intel $100-150 CPU Benchmarks - Gaming
Then spend the rest of your budget on the most expensive video card you can afford.
There is absolutely no reason to spend over $220 on a CPU, let alone $150. In fact, you might even want to go a bit lower than a 9xx or Core i3, allowing you to put even more budget into your video card. An X2 550 is a good choice, because although it's dual core, it has a full sized cache and high clock speed. This is more important than having more cores in games, and that extra $50-70 will be much more effective in games when put into a better video card.