Help with a build for a friend

[DarkMassacre]

A friend of mine needs a new computer, one that can play games at least decently well. She needs everything, monitor, mouse... Everything, except an OS. She doesn't want to spend over 800 dollars if it can be helped. Anyone have some recommended parts?

 

[Muffin Man]

Newegg.com - Computer Parts, PC Components, Laptop Computers, LED LCD TV, Digital Cameras and more!
Newegg.com - Computer Parts, PC Components, Laptop Computers, LED LCD TV, Digital Cameras and more!
Newegg.com - Computer Parts, PC Components, Laptop Computers, LED LCD TV, Digital Cameras and more!
Newegg.com - SAMSUNG Spinpoint F3 HD502HJ 500GB 7200 RPM 16MB Cache SATA 3.0Gb/s 3.5" Internal Hard Drive -Bare Drive
Newegg.com - COOLER MASTER Elite RC-310-BWN1-GP Black Steel / Plastic ATX Mid Tower Computer Case
Newegg.com - Hanns·G HZ201HPB Black 20" 5ms HDMI Widescreen LCD Monitor 250 cd/m2 X-Contrast 15000:1(1000:1) Built-in Speakers

totals $734 + shipping.

as far as keyboard and mouse; ive seen this one suggested before.
Newegg.com - Logitech MX 518 8 Buttons 1 x Wheel USB Wired Optical 1800 dpi Gaming Mouse

not sure about keyboards though, might need some help from someone else to suggest one.