If you want to play newer games, you should invest into a cheap dedicated GPU. As for the processor an i5-2400 will fit in your budget. Don't get a coolermaster, look into Corsair/Seasonic/OCZ/Antec Earthwatts PSUs.
CPU - i5 2400
MOBO - ASUS P8H61-M LX or ASRock H61M-GE (both are viable options)
PSU - SeaSonic S12II 620 or CORSAIR Builder Series CX600 if you're intrested in a $20 MIR
Memory - 8GB since memory is so cheap.
Case/HDD/DVD - personal preferance really.
I would recommend a Hard Drive that runs at 7200rpm (rotations per minute), is from the manufacturers Western Digital, Seagate, and Samsung F3/F4 (Hitachi is meh), and has a decently-sized cache, all within your budget of course.