Yes the kit I worked on did have a wrap, which required a lot of sanding and prep work before I could put a finish on.
If the kit you're discussiong didn't have a wrap I will assume the surface of the shells are in decent condition. If you go with paint, (vs. a wood stain) I would suggest a gloss or semi-gloss. I can't recommend a specific brand - read the cans to determine what is recommended for application to wood. If you go to a reputable paint/hardware store there should be someone who can make recommendations.
If you know the type of wood your looking to paint, relay that info to the paint store rep. (drums are normally maple or birch on the high end and mahogany or basswood on the low end). If you don't know, take one of the drums with, if you deal with someone who knows his stuff, he should be able to identify the type of wood.
The key thing with stain or paint is to properly prepare the surface, use several thin application (vs. trying to put it on thick in one pass) and after the final coat of paint is applied, veneer the surface with some type of poly coating to protect the surface. Obviously be careful not to compromise the baring edges.
Good luck.