Black or charcoal would be safe choices. A bit more out there would be grayed greens, grayed purple or similar.

I guess it depends on your personality. And small color cues in your shingles or things you love. I see blue (could be the photo) in the shingles, so any hue of cobalt would be interesting to see. Being there is a rust color in the bricks, the color of the door now looks nice. If you want a faux wood look, which I've done on a fiberglass door and it looks cool, I'd recommend everythingicreate.com for tips. Black would look refined and beautiful, but it might fall into the background and make your garage the focal point of your home. Could you upload your photo into Windows Paint and "paint" different colors into your photo to test?

You may also consider faux painting the garage door to match the front door, omg that would look gorgeous!

Like Kristin mentioned, using the blue in the shingles to your favor… I would suggest a dark blue, maybe Loyal Blue by Sherwin Williams.

You have some beautiful gray and cream elements on the house, so with that neutral palette you can do many things. I'm not seeing any green tones work well though . . with the black shutters so near. Black would look super from the street . . but that may be so obvious that . . . if you wanted those you probably wouldn't ask .. . what is the accent color that you use inside? Yellow is out as it will clash with the tan, green would have to be just the right shade - - a strong kelly green would work. Blue doesn't do much for me unless you want to redo shutters also .. this house is classic enough that a clear strong red . . heading towards the red-orange family would be terrific. test bm cochineal red http://www.benjaminmoore.com/en-us/paint-color/cochinealred