I had asked a few auto body places, and they were quoting figures anywhere from $150 to $500. "The wood will soak up the paint, see? So it won't work."
I think if the wood were primed right it would work out okay, but I think I'll let the wood guy give me some answers.
*note* I'm not a wood guy, but I've done this thing a few times with pianos.
Yes, the wood will soak up the paint. That's why you use a lot of coats. Have those guys ever seen the glossy smooth finish on a piano? Of course it works

Your guess is right, it takes a lot of sanding beforehand, and a good coat or three of primer. It also takes a lot of sanding between coats, a lot of coats of paint (car paint works very very well), and it takes a lot of clear coats as well. Sand the bare wood a lot (up to or past 600 grit), clean the surface with tack cloths every time you do something to it, use a lot of coats, and do a lot of wet sanding/wet steel wool between coats, and follow it up with a lot of clear coats or glazing. It takes a lot of time, but it can be done if you start with good stock and pay a lot of attention to sanding and cleaning.