If it was me, instead of a deck I would put a larger concrete slab in. My patio runs the length of my house and I love it, they can play when it is wet, ride riding toys, play with chalk, etc....off subject sorry
I agree with the mulch; easy care and when they cart around you can just sweep it off the deck (speak from experience here...) They seem to have waaaay more fun with mulch than sand! lol.
I have rubber mulch and I love it. It's pretty readily available now at home improvement stores (I got mine at Ace hardware). No bugs, no splinters, doesn't fade or rot. The only downside is it can get hot if in direct sunlight for a large portion of the day.
Btw, I love your back yard even if it is small
