How thick should the slabs be?
Always, the thinner the better. The challenge when you cut slabs very thin is that they usually warp. You need good stable burl wood to begin with, and make sure all sides and surfaces are sealed so that too doesn't put stresses in the wood. I'd recommend storing them under pressure to keep them flat.
How big should the diameter be?
For diameter, the slab should frame the pot and tree. The common issue here is that people use too small a slab and the piece looks crowded on it. In general, the thinner the slab, the bigger it can be.
You can even use a larger thin slab as the platform for an entire display, where the shohin is on it's own little table, and the accent is on a tiny slab, and both are arranged as a unit on the larger slab. I've seen some nice redwood slabs with multiple flat areas used effectively. They also use black lacquer rectangular slabs for this, for a bit more formal display.