Older MoBo newer cpu

If you're talking about the GIGABYTE GA-965P-DS3, then the motherboard will support all Core 2 CPUs except the Core 2 Extreme QX9770. However you might need to flash your motherboard BIOS before your motherboard will recognise any of the processors. The latest BIOS available is F14.

If you live a Micro Center, then I recommend a Core 2 Quad Q9550 for $170, pick this if possible. Otherwise the Core 2 Quad Q8400, or if you're not looking for a quad core the E7500 or E8400 are good choices.