there is plenty you get get on both the Pre-built end and the DIY end, of course either way you'll have to do some work, to get a good deal on a pre-built PC you'll have to do some searching, if you buy one as full retail price you're getting ripped off hard.
something like:
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227506
this is a decent pre-built value, a strong i5 haswell processor with a 7850 which should play all the games you mentioned at medium settings and probably even higher (on 1080p of course), comes with a cheap mouse and keyboard, but they are both at least usable so no problems there, and all you have to do is spend the last 150 bucks (assuming you didn't include tax in your figure) on a monitor and you're good to go.
Another slightly more complicated thing you can do is buy a cheap pre-built on a deal that doesn't have a discrete graphics card in (OEMs often do this for their home consumer low end builds, they stick in like an i3/i5/i7 and leave out a graphics card to give the illusion of it being a great price), then buy your own graphics card (and maybe PSU too) and stick it in.
The advantage to building your own is balance of components and sales, you can have individual parts on sale to keep the entire cost down, while a pre-built can only be on sale or not on sale. And pre-builts often come with usable but questionable parts in the places people don't usually look, like generic RAM, generic PSU, generic hard drive, etc.
And now I present what you can build with $950:
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: Intel Core i5-4670 3.4GHz Quad-Core Processor ($209.98 @ SuperBiiz)
Motherboard: Asus H81M-A Micro ATX LGA1150 Motherboard ($62.62 @ NCIX US)
Memory: GeIL EVO Veloce Series 8GB (2 x 4GB) DDR3-1600 Memory ($62.99 @ Newegg)
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive ($46.96 @ Amazon)
Video Card: Gigabyte GeForce GTX 760 2GB Video Card ($249.99 @ NCIX US)
Case: Fractal Design Core 1000 USB 3.0 MicroATX Mid Tower Case ($39.99 @ Microcenter)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($44.99 @ Amazon)
Optical Drive: Samsung SH-118BB DVD/CD Drive ($13.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($88.99 @ B&H)
Monitor: Acer G236HLBbd 60Hz 23.0" Monitor ($109.99 @ Amazon)
Total: $930.49
It's not too much different, basically just a stronger graphics card. The only way you can beat a DIY price with a pre-built is if you get a killer coupon from a manufacturer, but those only happen once in a while so it takes some google-fu to make it happen.
Facebook
Twitter
Instagram