The support lumber for the deck, other than the heavy posts, should all be above the ground. Even though you'll use pressure-treated lumber, it must all still be above the ground so that it lasts a long time. It will be difficult to repair if it ever deteriorates.
If the lumber does touch the ground, it may not rot, but ground moisture will make it unstable, causing warpage and movement. The only movements that you want on your deck are friends dancing at your next party.
The proper solution to your dilemma is a grade beam made from poured concrete. This is usually poured in an eight-inch-wide trench that's about one foot deep. This portion of the job should be left up to a professional. Once the grade beams are ready, you can do the rest of the work yourself.
You'll need a minimum of two concrete-grade beams and more for a large deck. If you live in an area with freezing winter temperatures, they should be set on concrete piers that extend down below the freeze line. The piers should be spaced about every five feet and flared out at the bottom.
Since your yard is sloped, one side of your deck will be above the ground level. Continue the grade beams across the entire deck area anyway. It can get difficult trying to match up a wood post to it. For a better appearance, position the outer grade beam in from the deck edge so that it's hidden from view.
When you select the contractor to dig and pour the grade beams, make sure that they plan to use steel reinforcing rods in the beams. They should also install vertical anchor bolts at least every six feet. Eight-inch to 10-inch long, 1/2-inch diameter bolts are commonly used, and they should extend up at least two inches.
The tops of the beams should be smooth and level, and all beam top surfaces should be in the same plane. Check this with a string and a level before proceeding. If it wasn't done properly, you'll have nothing but headaches with the building of the rest of your deck.
Lay two- by six-inch or two- by eight-inch treated lumber over the anchor screws on the top of the beams, and secure them in place. The remainder of the deck construction will be similar to any other deck.
Since your deck is relatively close to the moist ground, definitely use stainless steel screws to assemble it. Don't lay plastic film on the ground under it. This will likely allow rainwater to stand, which creates more moisture and breeding locations for mosquitoes.
While you're purchasing your fasteners, consider using special decking screws. They're knurled above the screw threads, so they bore their own pilot hole. This design nearly eliminates the problem of snapping a screw when you install it.
It's extremely important to seal all of the wood with a good synthetic type of wood sealer before you begin to build the deck. With it being so close to the ground, you won't be able to treat the underside again. Without sealing underneath, too, the decking will surely cup if it's exposed to the hot sun.