Also I should mention that I want to paint the garage door and I guess it will depend which way I go with the brick but would love suggestions on that as well!

I dont usually suggest painting brick, but, in your case, I would paint that brick and the siding the same color. Pick a color from the beautiful stone that you have and paint the house and the brick to blend in nicely with the stone. I dont recommend staining in your case, nor even a wash on the brick. It needs to be all one color for your house to look cohesive. Make sure you use paint that is meant for brick.. Brick needs special paint, because, it needs to breathe. Regular paint, will just end up peeling and looking bad.

I would stain. Stain lasts a long time and doesn't flake like all paints do eventually. I would pick one of the browns from the stone.