Following radeons should do a good job
They all have low power usage and should work fine on your 350W PSU (As long as it's a make of decent quality)
For any form of gaming, stay clear of 4350's, 5450's... They are great strictly for office productivity, in other words, adding a second screen...
(Still beats an onboard 4250, nvidia 8200 or Intel HD but you are limited to very old titles or very low details)
I personally played Mafia II on the following specs at a friend's place. (It's their spare HDTV PC)
Athlon II X2 2.8Ghz
2x1 Gigs Ram
The game looked great on 1920x1080 with medium graphics... I was quite impressed.
Did lag at times but overall was good.