You don't have room for posts.
What is your foundation? Are you using Sonotubes or precast blocks laid on the ground?
Personally, I would use the precast blocks. Excavate the topsoil where each one will go and fill the hole with compacted limestone for a base for the blocks and set them so they are at the right level for the beams. Remember to slope the deck beams a minimum of 1/8"/FT away from the house.
In either case just set your beams on the piers and use joist hangers on the sides of the beams. You need to do this to keep the height down to your 1 foot.
Sizing beams depends on the distance between piers and spacing of beams.
Sizing of joists depends on length of span and desired load factor and species of lumber.
Spacing of joists depends on decking material and desired stiffness.
Code and standard practice require 40#LL and 10#DL L/360.
If we start with actual 2x PT lumber for decking and a 12" joist spacing, you already have a very stiff deck, so the only variables left are the joist span and beam spacing and pier spacing. But you will see that 12" spacing isn't required.
To avoid having to install too many piers, you have set the piers at 7' spacing. To keep the beams from being too deep, the only other variable we can adjust, is the spacing between beams.
First, let's get the orientation right. I would run the deck boards perpendicular to the wall of the house. That way, using 14' boards, there will be no end joints.
This means the joists will be parallel with the house.
2x6 joists in hem/fir at 12"o.c. will span 10' with a 40#LL and 10#DL. Not quite enough if you split the 22' in half with a beam. But if you use SYP (Southern yellow pine) or doug fir, it is adequate.
If you use 2x8 joists in hem/fir, you can easily span with 16"o.c. spacing.
This means 3 beams running perpendicular to the house wall, and 14' long.
Again, using hem/fir, 2-2x8's will span 7'6" with the beams spaced at 12'.
Because you need support at the beam ends at the house, I would not use a ledger, but instead, support the beam ends with piers and build the deck independent of the house structure, avoiding the problems of a ledger board.
Using joist hangers on the sides of the beams, will keep the joists in the same plane as the beams, and keep the overall depth of the deck structure to 8 3/4". This will keep it up off the ground enough to keep it from rotting, and allow your piers to protrude from the finish grade a little.
So you will need 9 piers, 6 2x8x14's for beams, 24 2x8x12's for joists, about 48 2x6x14's for deck boards and 48 joist hangers. Plus nails, screws and stain.
Sizes are taken from a deck span chart here:
http://parkeronline.org/DocumentCenter/Home/View/732
This is all figured in hem/fir. In NC you may have SYP available, which will make the structure even stiffer and stronger.
Do you understand all that I am telling you?