It should definatly do the trick, I think it would do the job even on full graphics for those games. Of course it would depend on things like your chipset, and amount of ram u have. I run something compareable, radeon 9600 pro 256 mb, AMD 64 3200+ 2.2 ghz, 1 gig of ram with an Nforce3. It can run these games perfect.
If your worried about playing full performance, just buy a bit of an older game first, to make sure it runs well. Like Bf1942, call of duty ect..
If they run to your standards go ahead and get doom3, farcry, or halflife2.