while I love black for doors, do you have enough light coming in to keep things bright? Will you be doing the sidelights as well?

Look into BenMoore, Advance. It's the best paint for wood. Make sure you seal that wood with a dark gray primer, prior to painting it a color. (give it a light sanding and cleaning prior to the primer). Personally, I would to a fine sanding of all the wood to be painted. clean well to remove any specks. Then use a spray shellac (non-waxed by Zinsser) to seal up the pores of the wood. Once dry, run your hand over the wood. If it feels a little rough, very lightly smooth w/a 220 sanding block. wipe clean. Now apply the gray primer. When that dries, smooth again w/a 220 grit. wipe clean, now you can paint. Seem like a lot of work? Not really. But it will make the difference between a meh paint job and a really good one. Black shows every boo-boo so your prep is major for this.

Have the paint mixer manually tint the dark base with only the black tint. On their color chip cards, their blackest 'Black' isn't really "Black". If you want a deep, rich black, have them manually tint it with just the black tint. I had a number 4 base, in a quart can, and he shot it with 4-5 squirts of the pure black tint. It's a perfect pure black.

If you only have Behr paint, then look at the color 'Beluga'. I did one of my walls with it.

My personal favorite is PPG Paint's Black Magic 1001-7. Black interior doors are stunning.