Here in Ct the footings go 42" deep and I am sure that is true for NJ.

I would avoid burying posts in concrete and use a post base (http://www.strongtie.com/products/co...A-ABE-ABU.html) set over an anchor bolt cast in the concrete which keeps the wood away from the water. Local lumber yard in stock.

Joists could all be 2x8 and if you add a cross brace each way from each corner post (4x4 is fine) you might not need to attach to the house. I would make a perimeter of doubles that are bolted to the posts with 3/8" galv bolts and even notch one of the doubles into the post.

44" above ground requires a rail (anything over 30") so plan for one as a 44" fall is not fun.