What type paint for this Project

You could try concrete paint or stain for the stone and I prefer oil based paint for my exterior doors.

Concrete stain is the way to go. Paint will peel eventually, but stain is forever.

if you use paint cover with marine varnish lasts a long time

As far as the door goes, theres special paint just for doors. Its really designed to stand up to heat and uv rays and can take a serious beating as well. Good luck!

I would hous a good concrete stain, easier to do than painting and you can pick your color. I would also seal it with Spar varnish

The door can bepainted in several ways.. if it is a metal door, you can spray paint it with Rustoleum. I did that and it lasted for years, until I got tired of the color. When I repainted my door, I primed it withZinser 123 and then used a paint sprayer with latex paint. It still looks good several years later. My backdoor I did not want to take off the hinges, so I primed it and used a small roller and latex paint.