First issue is money, I don't have any, so I can't pour a slab, it's got to be on concrete piers or treated skids (or sleds, runners or sleepers, whatever you call them). What I would really like though is to build it so that the foundation isn't raised up six inches off the ground. Is this possible?

I live in Phoenix, so it's pretty dry. Would it be asking for too much trouble if I just built the floor frame of treated 2 x 6s and set them directly on a bed of two or three inches of gravel? If foundation stability is an issue, I could include some buried concrete blocks in the gravel.

I was hoping the gravel would be enough for drainage (when it happens to be one of the 10 days a year it DOES rain) and the joists would be enough for critters to keep out. (My brother had a cat die under his shed a few years back, that was NASTY.)

I just really don't like to look of raised sheds with a gaping hole underneath, but if I must, I must. Guess I could throw on a lattice skirt . . .

Until it rains.

A grade level foundation when you build is not likely to stay there over time (very few structures rise over time, except maybe a basement in Florida).
That would make your shed a low point, and water WILL find it.