basically any computer will work, it matters if the editing system will work. if you choose to go to windows 7, i believe you have to convert the video with windows movie maker (very simple editing system, nothing special.) if you choose to go to get a mac like suggested above, then it comes with imovie. which is again the same deal as windows movie maker, just works a lot better with a gopro. i personally edit on a pc and you sony vegas pro 9.0. with a mac you can get final cut pro, final cut express etc.
it really just comes down to if you want to spend a lot of money on a mac and get wicked editing programs, or spend less money and still get pretty dope editing programs with a pc.