[pushkins]

If your attaching a ledger board against (and to) the house then you don't need the two red posts.
The two beams (tan) will need to sit on the ledger or be attached to the ledger with Simpson hangers. as should the two outside rim/band boards (black).

I'm assuming that your floor joists will be on 16" centers so that makes it about (from the number of joists in your picture) 10'6" out from the home your beams (tan) will need to be min. 2x10" (I'd use 2x12").
Your floor joists will be supported by the beams 14' apart so I'd go with 2x12" floor joists as well.

You could and it might be easier for you to put a 2 x 2x12" beams (or a single LVL) on the two black posts, a 2x10" ledger on the house and run 2x10 floor joists out from the house (sitting on the ledger or joists hangared) out to the 2x12" beams/LVL, this would enable you to run your decking boards parallel to he house and if you wanted it would also allow you to have up to a 24" overhang on the posts.