I'd add to that, considering the Phenom II 965 is now cheaper than the i3. Its the better buy, its going to perform about the same in gaming as the i3. All of the benches that are done are done with video cards and graphics settings that exceed the capabilities of mid-level graphics cards. And for the CPU intensive stuff the OP wants to do, (the editing) the Phenom II is going to excel there. A cheap CPU cooler will easily allow you to overclock it to 4.0GHZ (and at least here in the US a Phenom II 965 $110 from newegg + $20 for 212+ Cooler) is going to cost $5 more than an i3, and well worth it IMHO for the superior multi-threading performance.
But the benches really are irrelevant anyway since any COD game with my 550 TI easily maintains well above 60FPS, and anything on the market can pretty much max out minecraft.
A quality 500 watt PSU is sufficient for the setup. The Cinebench score for an i3-2120 running 4 threads is 3.23. My Phenom II @ 4.0 scores 4.72. So the multi-threading difference is substantial.