If it has a beautiful wood grain then have it maybe stained and polyurethane or just polyurethane. If not and you can take it off the hinges for a few days or just leave it open for a few days, then a coat of good oil based primer and then oil based semi-gloss would be the best most durable finish You can get some Japan-Drier to make oil based paint dry quicker. If you can't leave it open or off the hinges, get some Zinsser Cover Stain which is a good quick drying oil based primer and some Benjamin Moore MoreGlo or Sherwin Williams equivalent Semi-Gloss latex but I would still recommend leaving it open overnight to keep it from sticking to the frame and pulling off the paint. One coat of Primer and one coat of paint will do it provided you have the same color.
I agree that an oil based stain will give you the best results. If this is a new prehung door you should be able to remove the weather stripping that runs around the door jamb. It should just pull out with moderate effort and can be replaced when the door is dry using just your fingers, but possibly may need to utilize a screwdriver or '5-1' paint tool. This should allow you to shut the door before the stain/paint is totally dry. Pulling the hinge pins and laying it flat will give you the best results, especially if you are planning on using a polyurethane. A mahogany door is very heavy and would be best removed and replaced by two people. If you opt to stain it in place just be sure to protect your floors with some plastic sheeting or even a large trash bag.