The reason there are soil engineers is that there are so many different types of dirt out there and what it can carry varies by a considerable amount. Then there is frost heave, where the ground gets wet, freezes, expands and the building moves. The reason you have basements up north is because you have to go down so many feet to get to stable ground and since you are already that deep, you might as well make a room out of it. Depth of your footings is based on how cold it gets there and how far down the ground freezes. Here in my part of Texas, a foot is plenty because we don't have that problem. The size of the footing is based on the load it will carry and how much weight the dirt will support. Some types of clay are very good for building on top of, others are terrible. If it's good stable clay, like red clay that I have here, a 2x2 footing at each corner would easily support the load of your room.
Another thing to consider is the size of your floor joists. The farther they span, the larger then need to be. For the exterior, load bearing walls that will support your roof, you need to either size your joists accordingly for that span, or add another footing midway to carry that load, which will allow you to use smaller lumber for the span.
When I do a room addition for a client, I decide if pier and beam is better over a slab. If the ground is fairly level and I don't need to add a lot of fill material, I prefer a slab. My footings are usually a foot wide and a foot deep with two layers of rebar through the footing all the way around the room. Rebar on 24 inch centers or less for the slab, which is 3 1/2 inches thick.
If the ground is sloping away and it's not practical to add material to build up the pad, I go with a pier and beam. I prefer a continuous footing around the perimeter of the room, and then either build up from my sill plates bolted to the footing, or I build up a wall to the height of the floor, then install my floor joists and go up from there.
I've seen posts used for rooms, but I've never done that.
Eddie