The following is an example of an inexpensive gaming system.
Fractal Design Core 1000 FD-CA-CORE-1000-USB3-BL Black Steel MicroATX Mid Tower Computer Case
Model #:Core 1000 USB 3.0
Item #:N82E16811352032
$49.99 -$10.00 Instant $39.99
There are lots of inexpensive case choices. By reputation, I would assume Fractal Design to be a little better/sturdier than many typical cheap cases, although in the past I have been very satisfied with low-end Rosewill cases. Often $10 cheaper and/or with free shipping, those seem to be mostly discontinued or out of stock now.
ASUS P8B75-M LX PLUS LGA 1155 Intel B75 SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard with UEFI BIOS
Model #
8B75-M LX PLUS
Item #:N82E16813131887
$69.99 $69.99
This board has modern interfaces, so it ought to remain viable through at least a few future upgrades.
XFX FX-775A-ZNP4 Radeon HD 7750 Core Edition 1GB 128-bit GDDR5 PCI Express 3.0 x16 HDCP Ready Video Card
Model #:FX-775A-ZNP4
Item #:N82E16814150612
$119.99 -$30.00 Instant $89.99
Can play any game, particularly at lower resolutions. For only $10 more, you might find a HD7770, which is substantially stronger.
Antec EarthWatts Green EA-380D Green 380W Continuous power ATX12V v2.3 / EPS12V 80 PLUS BRONZE Certified Active PFC Power ...
Model #:EA-380D Green
Item #:N82E16817371033
$59.99 -$15.00 Instant $44.99
Has been my "goto" PSU in budget builds for years. Reliable, efficient, and quiet, it will handle a future graphics card upgrade to any card needing a single 6-pin PCIe power cable.
Intel Core i3-3220 Ivy Bridge 3.3GHz LGA 1155 55W Dual-Core Desktop Processor ...
Model #:BX80637i33220
Item #:N82E16819116775
$129.99 $129.99
You could save more money and get a G860, but as games become better threaded, that is becoming a worse idea all the time. This hyperthreaded dual-core should be able to play games for at least a few years.
G.SKILL 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10600) Dual Channel Kit Desktop Memory Model F3-10600CL9D-4GBNT
Model #:F3-10600CL9D-4GBNT
Item #:N82E16820231253
$36.99 $36.99
8GB would be nice, but on a budget, 4GB will do. I've had good results from G.Skill.
Western Digital WD Blue WD5000AAKX 500GB 7200 RPM 16MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive - OEM
Model #:WD5000AAKX
Item #:N82E16822136769
$59.99 $59.99
Typical consumer drive. Large enough to hold a decent variety of applications and games, plus lots of data. If you don't work with video, you may not need to upgrade this ever.
LG 24X DVD Burner - Bare Drive Black SATA Model GH24NS95 - OEM
Model #:GH24NS95
Item #:N82E16827136259
$18.49 $18.49
Meh. One optical drive is much like another.
Subtotal: $490.42
Add the operating system, monitor, mouse, keyboard, and/or speakers if you don't have them.