Yes, 16 would be the way to go, if not 24.  Definitely check out Boss/Roland above all else for a self-contained 16 track system. They've got a new one out that is excellent.  It does it all. Records, mixes, effects, and has some mastering.  Finally it will burn the CD with a burner attached to the unit.  I've been most happy with their stuff. I have a smaller unit, the 8 track BR 1180 and it's very decent for home recordings or demos.  Lemme look up the model number of the 16 for you.

Gene

P.S.  Check link below.  I believe this is a unit you would be very pleased with.   Reasonably priced considering the number of features. Another thing about their products, is that they're very user friendly.  You should be up an running fairly quickly with this one.

http://www.musiciansfriend.com/srs7/g=rec/s=recorders/search/detail/base_pid/241064/