Branching, opposite/alternate, compound/simple? At what size are the leaves simply too big?
You look for the exact same things you'd want in a non-native species like Japanese maples or Chinese junipers.
Branching doesn't matter, although alternate is a tad easier. Compound leaves usually
end up looking too large. And, leaves are too large when they no longer give you a "natural" feel -- and that
is in the eye of the beholder.
Run through the list of natives here on the ABS site that one or the other of us have used as bonsai, and you will find that the characteristics can vary widely. But if you look at a plant and immediately think, "Wow! That would make a nice bonsai", those
are the characteristics you want.