As we are seeing in games, CPU cores are being utilized more and more. Right now a few games already use more than 2 cores (Which is what the i3 has). So I would recommend a 4 core CPU (i5).
For the CPU I would recommend you get the i5 3570K, this is a 4 core CPU and it runs very fast. It is also the BEST gaming CPU, as anything higher is using hyperthreading and hyperthreading has no impact on games.
TLDR; Get the i5 3570K CPU ($220)
EDIT: As a side note, I would suggest you DO NOT skimp on the GPU. As it the GPU is the heart of your system in terms of gaming.