Also, the back of our house is not painted and has the old weathered, grayish look. Would a brown stain look ok with that?

I think I would do a more gray than brown stain and maybe the railing the same since it is not very pretty and when you do the new deck make the railings the black metal with glass panels For right now a dark gray soild stain for the deck and railing then maybe for now some planters hanging off the railing to liven it up a bit