The brick is very neutral and looks to be in great shape. I think it would be better to update the siding to a real wood or Hardie board.

The brick needs to be painted? Why? Is it in poor shape, needs tuckpointing or powerwashed?

If you decide to paint it, consider using paint specific for brick, not regular thick house paint.

First things first, power wash the siding, brick and sidewalks, etc. And then I agree with Susan's suggestion of updating the siding. Depending upon the color of the roof AND brick mortor, perhaps a charcoal, green, or navy blue siding would look great.

I agree on the power washing. I would not paint the brick. Why take something maintenance free, and paint it. I do agree, a charcoal would be very nice where the siding is, but, since you have vinyl siding, it cant be painted a dark color because, it would most likely warp. I would spend my money replacing the siding with wood, and then painting it a charcoal color.

I would paint brick as well.