So basically - if you want a better, more complete experience with the Final Cut package, and plan to use a mini, look for an early 2009 version mini or newer (the current new minis are 'late 2009' models). MacBook Air best for video editing on the move. The 2009 minis have a nvidia 9400m integrated gpu - yes, it's not as good as a dedicated gpu, but it's lightyears ahead of the intel GMA's, and you don't really loose functionality with FCS (aside from one certain feature of Color, which is more due to the minimum graphics ram it requires if I recall correctly) As you’ve probably guessed already, the Mac Pro is the ultimate Apple device for video editing and, probably.
The pre-2009 models had Intel GMA integrated graphics - the integrated graphics is not fully supported by Final Cut and you can loose certain abilities with the software (off hand I can't tell you which ones, but if I recall correctly it has to do with certain filters and effects, not including some of the additional programs that are part of FCS really need a more powerful GPU). Honestly, I wouldn't get a mini pre-2009 for video editing. There are many G4 minis out there, I'd stay away from them.