From the MythTV perspective, it depends. The video cards will do some video processing, but for the best "quality and options" you probably need a bit of a beefy CPU. The previously recommended minimum was a "P4 3.0 Ghz; 512MB RAM" which has been easily translated to an AMD64 3200 or a Core2Duo at about ~1.8Ghz (such as a Mac Mini). These are HDTV specs, SDTV specs are considerably lower, but I don't think the lowend threshold has really been identified (lately) as hardware with these specs has become increasingly available at lower costs.
HTH
-Chad