Hi, Susie. Sorry about the bad news. For a good finish that will stay on you need two things, a smooth substrate and a surface with enough "tooth" to hold the paint on.
If you are lucky enough to buy doors with a stain finish, you probably can wash with trisodium phosphate (TSP), sand lightly with about 150 grit paper, tack rag, prime and paint. If you must buy painted doors, you will probably have to strip the old paint off, sand lightly, tack rag, apply a primer, sand and tack rag, apply the paint.
For a primer with either finish, I suggest B-I-N. This will block stain from bleeding thru and present a good surface on wood.
Be sure to follow manufacturers instructions and safety precautions on any products you choose.