I think you can use any machine that fits on the carriage, even a vintage Singer. However, usually you want a machine that can stitch really fast, as this makes free-motion quilting easier and faster. For example, the Janome 1600P does 1600 stitches per minute, which is a lot faster than a vintage Singer. The bigger the throat, the better. If at all possible, you also want a machine where the bobbin holds more thread so you don't have to change the bobbin as often.
I found this website that may be of help to you:
http://www.superquilter.com/longarm.html
Also, if you join the homequiltingsystems group on groups.yahoo.com you can usually get lots of good advice there.