lemongrove
Any shade of grey would go well with brass door fittings, but how about a Cotswold pale green or rich cream? Or are there too many of this colour on neighbours doors already?
I don't believe you should paint the door to add a splash of color. I believe it will make the large arch appear disproportionate. Your home, in my opinion, is not appropriate for this particular trend.
I believe that painting all of the trim (including the door) a warm white that matches the windows would be a nice little upgrade. It isn't the same bang for the buck that a brightly colored door could provide for a different style of house, but it would be an upgrade, in my opinion. Here is a guide about paint for front door.