Hi Bradley,
First you need to determine what type of paint is already on the existing cabinets. One way to determine this is by looking inside the cabinets (assuming the inside has been painted) if the paint has significantly darkened or "yellowed" then the finish is likely an Alkyd (oil based) paint.
Another way is to pick up some denatured alcohol at the hardware store, daub some on a rag and rub the finish. A latex finish will become sticky and transfer quickly to the rag, alkyd will not transfer, with the exception of a small amount of "dead" paint. Once you determine what type of paint you have stick to it for the new doors.You may want to remove one of the existing doors and take it to the paint store for a color match.
Prime the new doors, in this case I recommend a solvent based primer such as solvent Kilz or Coverstain. You may need to prime the door edges twice. Sand the primer smooth with 180 - 220 grit sandpaper. Finish with two coats of finish paint, sanding between coats.
Hope this helps
rmichael pro painter