Instead of tell you what you should or shouldn’t do – I’ll just try to answer your question. As the previous posters already said, it will work. I personally run Final Cut Studio 2 on my first gen MacBook and it works fine. Color WILL install, however it will not run because of the graphics situation. Final Cut Pro 6 works just as good as Final Cut Pro 5.
And also to shed a little more light regarding the single firewire bus that the first responder mentioned–even though my firewire drive and deck share 1 firewire bus, I’ve never have had any problems during capture, playback, and lay-off. In theory there could be problems, but in a year plus using this machine to edit DV, HDV, and even some DVCPRO HD 720 footage on and external firewire drive while using a DV deck, I’ve never had any problems with stuff that was rendered on a timeline.
So while there are definitely much better options out there as far as hardware for running FCS, the mac mini should work without problems.
Hope this helps. Peace.