Homebuilt Game PC

should be fine. More and more games are multithreeaded however, so for about the same price, I'll suggest an A10 or FX4300, or for a bit more the FX 6300

Im new to this, so could you give me some information and maybe suggestions

That looks like a solid entry level gaming computer to me. I would suggest a more powerful CPU at some point. An Intel 3570 or 3570K if you want to over clock is a good choice. If you can't afford that a good next step down is the 3350P. Most newer games right now are written to take advantage of 2-4 cores. I think it will be at least 3 years until games start being written to take advantage of more then 4 cores.

If you're interested here is the Tom's article on the Best CPU's for the the month of January: http://www.tomshardware.com/reviews/gaming-cpu-review-o...

It looks reasonable to me. Which i3 were you thinking of? 3220?