I'd paint it blue or red, but black is classic. If you're not sure about black, you could try dark navy.

The house is already dark, i would go with a lighter color, even the same wood finish but more on the colder side, or maybe a blue or greenish light finish

The wooden door doesn't match the gray.

I agree that black would "blend in" well and would play nicely with the gray. You want the front door to "stand out" a bit /direct people towards the entrance. Black won't really do that. Typically I'd say the gable would direct people towards the door, but you have an awful lot going on here, and I'm not sure that's enough.

Personally, I'd paint it a brick red. (Of course, I almost always say red front door.) Red will blend nicely with the gray, and it'll be eye catching enough to draw guests to the right place. Then supplement with some red flowers or other accents.

A shiny black door could be nice. I’d probably want some white trim around it to set it off more. Not a big fan of red but agree it would bring more focus. Mrs. Pete’s suggestion of red blooms and accents could also help.

If it is real wood, I would get a door refinished to come in and have it refinished in a darker/deeper/richer stain color.