i've got a 13" 2009 mbp with a 2.53ghz processor, geforce 9400m with 256mb of ram and 8gb system ram - so it should be pretty similar to your mini.
all versions of final cut work on this machine.
older versions of fcpx should work on snow leopard and you can get the latest version running if you update to mavericks.
this computer is too slow to really enjoy editing of native hd footage in fcpx - but you can work around this by using proxy files for the actual cutting - they work just fine. it's definitely to slow to cut h.264 files natively. sd runs fine as well.
fcp7 is noticeably faster (and way more feature complete), but it's also showing it's age.
i mostly use fcpx on it, when i have to do a quick cut while away from my main workstation, using proxy files. if you're planning using the mini for more than the occasional edit, i'd definitely go for fcp7.