Read this website for best gaming cpus for the money.
They update it once a month.
At that price I would recommend a 2 core/ 4 thread Intel i3 2125 = $120.
A 4 core i5 2300 starts at $160 is much much faster and a better deal than an i3 IMHO.
As for mb there are too many to chose from so stick with a socket 1155 board from
ASrock, Gigabyte or MSI.
I would try to get the Seagate Momentus XT Hybrid SSD 750 GB HD, it is about $200, nearly as fast as an SSD and much easier to deal with than managing 2 drives. It has a tiny SSD built into the HD that does a good job of remembering what you use most often. I put one in my girlfriend laptop (guinea pig) and it works great.
Although Radeon cards are cheaper, Nvidia has better drivers and support (= quality).
You get what you pay for.
I always am happiest with GeForce over the few Radeons I have tried.
The GTX460 is a good cheap card = $100, but I suggest the newer 560 at $150.
Do not go lower than the GeForce 450 or 550 = $120.
I use EVGA for the lifetime warranty, but I have never had one fail and I do overclock them.