Home Depot clerks aren't exactly the best place to ask a painting question, but hey at least he didn't lie and give you some answer that would have been his best guess. You should use 100 percent acrylic paint, exterior paint for the exterior side and interior paint for the interior side. You can find paints that are rated for both exterior and interior as well. I would use at least a satin sheen so that the door is durable and somewhat washable when you are done. You can spray, brush or roll, whatever your choice. I usually roll them with small mohair rollers or whiizzies. It's too much effort setting up the sprayer for one door IMO.

Thanks for the feedback. I believe I can find the back door and the garage door in the same wood species (they are right next to one another). I've been told that, with some effort, we can get the patio ceiling (likely pine) to stain close (but not exact) to the garage/back doors. Unfortunately, the front door we like is only available in Mahogany. The only variable that is near the front door is the front porch patio ceiling (again, likely going to be pine). I'm wondering with a lot of experimentation if we can get the Front Door (Mahogany) to stain close to the pine ceiling? Of course, all of this would be much easier if I could just find a single wood species that is readily available on doors, garage doors and tongue/groove planks??? Thanks again for your comment. I will consider painting the ceiling boards if we can make them match.

Well yes, my general question is references of people that actually know what they are doing and teach it? I found a couple in youtube but most are obviously amateurs and basically just video their learning experience. However, I have not seen ONE video discussing the types of paint products. You can be certain anything you get from a big box store like stains and such have no place on an exterior door. I think automotive urethanes are probably the absolute best for this, but those paints are designed to kickoff in seconds or "flash". It would seem like exterior latex might work, but......

Keep the exterior materials the same on all sides, don't stress about coordinating with the chrome interior.