Your posts should go ground (footing) to truss, if you want it to be "bomb-proof", which is the only way I like to build it. the deck beams then bolt through the posts, parallel to the house, then the deck joists would sit on the beams attached to joist hangers on a header on the side of the house. Make sure you flash your header properly to prevent water penetration into the house.
Beyond that, consider having your roof trusses built, for the same reasons I list under the response to the guy wanting to build a garage yesterday. Even though these are partial trusses, they will cost a lot less than you expect, and they will be done right.
Do lots of research here, and consider paying an architect to refine your design and save you a headache or two.
There is a good chance you will have to pull a permit to do a job like this anyway, so an architect's input will help that process.