I realize this is sacrilege, but I don't know where else to ask...

No reason to buy a prebuilt for gaming. You'll end up paying much more than necessary and end up with an overpowered CPU, underpowered GPU, more RAM than you'll ever use, and a disappointing gaming experience.

PCPartPicker part list / Price breakdown by merchant

Type Item Price
CPU Intel Core i3-4160 3.6GHz Dual-Core Processor $102.99 @ SuperBiiz
Motherboard ASRock H97M Anniversary Micro ATX LGA1150 Motherboard $67.89 @ OutletPC
Memory Kingston HyperX Fury Blue 8GB (2 x 4GB) DDR3-1333 Memory $41.99 @ SuperBiiz
Storage PNY CS1111 120GB 2.5" Solid State Drive $51.97 @ Amazon
Storage Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive $46.89 @ OutletPC
Video Card PowerColor Radeon R7 370 2GB PCS+ Video Card $143.98 @ Newegg
Case Fractal Design Core 1500 MicroATX Mini Tower Case $44.99 @ NCIX US
Power Supply Corsair CSM 450W 80+ Gold Certified Semi-Modular ATX Power Supply $56.99 @ Newegg
Operating System Microsoft Windows 8.1 OEM (64-bit) $88.88 @ NCIX US
Prices include shipping, taxes, rebates, and discounts
Total $646.57
Generated by PCPartPicker 2015-07-30 23:09 EDT-0400

Assembling the Components LinusTechTips has some good build guides,
as well as NZXT (https://www.reddit.com/r/buildapc/comments/2oblwp/nzxt_made_a_website_and_video_series_on_how_to/).

/r/buildapc Thread