Do it. Core i3 isn't the best but it's very very good for what it is, the hyper threading it has helps it a lot in games like BF3.
I agree, I was originally planning a very similar build myself. However, consider changing the B75 board to the ASRock H77 board, it's $69.99 right now, so the price should be the same, but it's more geared towards home users, whereas the B75 chipset is designed more for businesses (trades features you may want, such as SSD caching, for features that a home user won't need).
Edit: Btw, I think the i3 3220 is $109.99 at NCIX.com right now. Or at least it was last time I checked.
Yeah microcenter tends to have ridiculous in store processor prices on processors, or at least I know they do on like 3570k's and 3770k's. A rep there once told me their profit margins on those things are almost nothing, which makes since as they sell 3770k's for like $230 while everywhere else they're like $300+
This is the best combo for the price. The CPU is very good and the motherboard is awesome which has 8+2 phase VRM which is very good for overclocking, so when you have like 30 extra dollars, just get a CM Hyper 212 Evo and take that CPU to 4 - 4.2 GHz and at those clock speeds, it would be a beast in performance. The i3 does not even come close to the overclocked 6300. You can take that to about 4.5 Ghz if cooling is very good. Just go for this CPU at this price. It is a beast and when overclocked it is GOD !!!