I agree with the others here.
Your Mac Mini will be just fine.
In fact any computer you have will work, whether laptop or tower. Obviously, there will be machines that are better at it than others, but don't let "analisys paralisys" stop you. Just max out your RAM and HD space as much as possible and it will work.
Check the Dec 2012 issue of Sound on Sound. There's a great interview with John Palladino talking about recording Frank Sinatra in the late 50's. In the interview he talks about how, even while working with a big company like Capital (or was it Columbia?), they were always short on equipment, or had to deal with "crap-tastic" acoustics, yet they were able to make the albums that made people like Frank legends.
The point is, just use what you have to the best of your ability, and make some great music.
Carvin Club #167
Switch-Hitter #25 (musical switch-hitter you pervs! Musical!)