Well your single-core proc, and 1Gb or RAM will certainly bottleneck any card capable of maxing UT3, which BTW will not need a monster of a system Ala Crysis, Recommended specs are a 7800gtx/dual-core/2Gb of RAM. If you are simply looking for the video card, I get a 8600gts. Not because it's DX10 but because it has the power consumption of a 7600gt, which is important because I suspect your PSU is alittle weak, post wattage and +12v amperage please.
If you have a S939 motherboard you have the option of a cheap dual-core. Upgrading to an extra gig of RAM will help as well. These suggestions are optional. They will certainly help, but are not absolutely needed, merely strongly recommended.