Good $880 Gaming PC for youtube?

So i have $880 and i want to build a good gaming pc for running games like:
Black ops 2
Minecraft
Team Fortress 2
Counter Strike
Garrys mod
GTA 4
GTA 5 ( When it comes out on pc. )

I don't need an os all i don't want a monitor. And with shipping i want it to come out to $900 max.

Well, that's tough.

I'd suggest trying to find a graphics card, one built to handle the graphic needs of the modern to later games.

Well I'll do 2 builds, a Gaming Build & a Gaming/Editing Build (since you make videos)
Mid End Gaming PC $770
Case-Silverstone PS08B or Fractal.Design Core 1000 $40
CPU-i5-3550P $180
GPU-MSI GTX 660 Ti DDR5 3GB $260
Motherboard-ASRock B875M-DGS $55
PSU-EVGA 500B $50
RAM-G.SKILL Value 4GB $36
HDD-WD Blue 1TB $60
DVD Drive-LG 24x $20
M+KB-Logitech MK120 $20
Total=$690($790 w/win 7/8 premium oem)
Mid End Editing/Gaming PC $770
Case-Silverstone PS08B or Fractal.Design Core 1000 $40
CPU-i5-3350 $180
Cooler-Cooler Master Hyper N520 $44
GPU-Gigabyte R7 260X DDR5 2GB $140
Motherboard-ASRock B875M-DGS $55
PSU-EVGA 500B $50
RAM-G.SKILL Value 8GB $67
HDD-WD Blue 1TB $60
DVD Drive-LG 24x $20
M+KB-Logitech MK120 $20
Total=$681($781 w/win 7/8 premium oem)

Take what Damonday said but buy two HDD's one for games and general storage and one for recording things onto. Its a ***** and a half to run a game since its using disk writing to run it and record since it also uses the disk write speed up. That and general storage fills up quickly on one hard drive this way you also have all your footage in one place.