I think it's personal taste, but I like dark charcoal gray shutters with that color brick.

What color will the new roof be? A simple color scheme includes three colors, the base color at 70% (in your case that's the red brick) a secondary color at 20% (away the roof and shutters) and an accent at 10% (sometimes used as a bright door color for a point of interest, or it can be more subtle like the choice of hardware color). If you let us know what colors you like, it might help us give you great insight.

We are going w a charcoal colored roof. Any other ideas on shutter and door color? Also, should we keep the accents white?

I think the trims should be white, but the downspout should be painted as close as you can get to the brick color.