Are you serious about trying to use Final Cut Studio or just trying to get by the cheapest way? The MacMini obviously has a faster single CPU G4 but runs on a 5400 rpm disk drive. It only has 400 MB Firewire connectivity and no video support for Motion, as you aluded to.
One the other hand, your G4 dual 500 doesn't even come close to the minimum requirements for FCP Studio.
Honestly, you'd be better off the get an iMac G5 and try to make that work, but it's not the best solution, which I am sure you will discover sooner than later.