$250 to finish this Budget Gaming Build

[moogleslam]

I'm trying to put together an ultra cheap PC, in part using some components which I already have. It needs to be adequate for some gaming such as MineCraft, Diablo 3, iRacing.... probably nothing too taxing. My budget to finish it is.... as little as possible, but let's say $250.

I'm comfortable overclocking, but it's not essential here.

The good news is I already have the following components:
Monitor (1920x1200)
HD 6970 Graphics Card
HDD
Keyboard/Mouse/Headphones
OS (Windows 8.1)

I can also do without an optical drive. I believe that means I only need Case, CPU, Motherboard, PSU, Memory.

Is what I have below the best I can do for that money? Anything wrong with these components or any changes you'd recommend. Is the PSU enough?

Either newegg or Amazon is fine. Prices are from newegg after instant rebates:

APEX SK-393-C Black Steel ATX Mid Tower Computer Case
$22.99

ASRock H97 Anniversary LGA 1150 Intel H97 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
$64.99

EVGA 100-W1-500-KR 500W ATX12V / EPS12V 80 PLUS Certified Active PFC Continuous Power Supply 3 Year Warranty Intel 4th Gen CPU Ready
$39.99

Intel Pentium G3258 Haswell Dual-Core 3.2 GHz LGA 1150 53W BX80646G3258 Desktop Processor
$69.99

G.SKILL Ripjaws X Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model F3-12800CL9D-8GBXL
$39.99

Subtotal: $237.95

 

[Xibyth]

If you want a slightly improvable quad core rig
PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-4350 4.2GHz Quad-Core Processor ($89.89 @ OutletPC)
Motherboard: ASRock 970M PRO3 Micro ATX AM3+/AM3 Motherboard ($39.98 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Case: Rosewill Blackbone ATX Mid Tower Case ($31.99 @ Newegg)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply ($34.99 @ NCIX US)
Total: $236.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-05 10:34 EDT-0400

If you want Intel, this is slightly above budget, but leaves much more options for upgrade.
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor ($111.89 @ OutletPC)
Motherboard: Gigabyte GA-B85M-DS3H-A Micro ATX LGA1150 Motherboard ($42.98 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Case: Rosewill Blackbone ATX Mid Tower Case ($31.99 @ Newegg)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply ($34.99 @ NCIX US)
Total: $261.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-05 10:35 EDT-0400

If you plan on going to an i5 in the future, get the pentium for now. Your choices are good considering the budget.

 

[Rogue Leader]

You won't set any records with it, but that is a pretty solid build for $250.

EVGA generally makes great PSU's, that said their lower end offerings are a little lacking in quality, BUT at that price range many others are worse. I would say its good enough, just don't overclock it.