Coming from experience in building I would go the addition route. I think you will get better return on you investment down the road.
My folks just did a sun room. Slab on grade, wood stud walls and lots of windows. It is basically an addition meaning dry walled interior walls, ceiling, electrical etc.
As far as things to incorporate into the addition:
Electrical, gas for BBQ/future fire pit, water (even if you don't need it now, leave it in the wall and put a cover plate over it), ceiling fan(s), audio.
Just my $.02