Get the 1155 chip, the 3820 just isn't worth the price due to the limited overclocking options.
For gaming an overclocked I7 3770 will perform better, at a lower price.
The Hyper 212 EVO will delivery adequate cooling cheaper aswell.
And as for the 3570 instead of the 3770 for gaming, I would disagree. At the moment yes 4 cores is enough, but in the interest of future proofing and the new consoles coming next year, hyper threading will likely be a feature you will want.