Nursery pots come in fairly standard diameters: 12, 15, 18, 21 and 24 cm. Design the ring 3 to 5 mm larger than the pot rim so it drops in without binding. If you want one stand to take several sizes, use a stepped ring or a cradle with adjustable slats instead.
How thick does the material need to be?
How do you stop water damaging the wood?
Can a laser-cut plant stand hold a large floor plant?