Why do you think you need the i7? That's a substantial amount of your budget right there for threads you won't need. The "best" gaming CPU is the Ivy Bridge i5-3570K for ~95% of the gaming population, with the more expensive X79/Sandy Bridge-E i7-3820 being the best for the top ~5% who use two or more GPUs.
At your price-point, it is difficult to include everything you want, even with the i5. I would suggest the following: • Increase your budget to $1150-1250 • Drop the SSD • Drop down to an i3-3220 w/8GB ram + Radeon 7770/GT 650 ------------------
Going with the first option of increasing your budget, here is a quality build roughly along the lines you specified.
If you have a Microcenter nearby, you can upgrade to an i7-3770K for the same price, or grab the i5-3570K for cheaper.
Gaming is not ideal under the iGPU at any meaningful resolution with anything higher than the lowest detail settings, even with the Intel HD 4000.
It also wouldn't make any sense to pair a beefy unlocked quad-core like the 3570K with an anemic GPU like the 7770, which is why I suggest downgrading to an i3-3220 (or even downgrading CPUs while upgrading GPUs).
He most certainly does NOT need the i7-3770K, and could probably get away with the i3-3220 without noticing. -- Those who would give up Essential Liberty to purchase a little Temporary Safety, deserve neither Liberty nor Safety.