Instead of a deck, I would consider a pretty stone patio. I think it would better suit the style of your house.

you have a lot of space to work with. The main thing driving it is your budget.

why don't you call in a landscape designer and see what they come up with? you could have anything back there

replacing the sliders w/somethng like this, and a wood deck

this is a front, but you could apply it to the back too. deck w/steps, and large flagstone pavers.

BTW, Hows the front? here are some ideas for that. (if you've ever thought about painting the brick, look into all natural Romabio)