$60 computer off craigslist. $20 for a graphics card off ebay.
Windows XP
2.2ghz processor
1g ram
512mb graphics card that bottlenecks because I'm running PCI-E 1.0, upgrading from 128mb to this did nothing (actually dropped about 2 fps, but some of the features on the card are worth having)
I run SR at lowest setting around 30fps, and Dominion around 25fps. I do get occasional lag but nothing game breaking.
So don't go telling people they can't run Dominion because their SR fps is only 30. It's not a graphically intense game at the lowest settings. Shutting the sound off (not volume, disabling sound) works wonders for the fps. Not running music, other programs, or even cutting out all but the necessary services in msconfig will also boost your fps.
You don't need to blow hundreds just to get a system that won't get you roflstomped. I'm sorry, but I get tired of people saying/implying this. No, it's not gonna look pretty. But I truly enjoy the game without shadows or sound, because of the game itself.