You can mix oil based primers and latex paint. The benefit to the oil primer is it won't raise the grain as much. I would stay away from latex in the kitchen though. As others have said it is gummy. I would use a pigmented solvent borne finish - lacquer or even better, conversion varnish. They are much harder and suited to the task. You should completely strip the old finish and sand the doors prior to refinishing. IMO stripping and sanding is so labor intensive, its almost better to just have new doors made, but if you have the time and not the money, then sand away.