I've never had good luck buying large wood screws. They would break. What is a good brand?
Tightbonds own web site rates III with a higher psi rating than II. Both are excellent but III will leave a darker glue line if that matters.Don't underestimate the power of PVA glue. IE Tightbond.
Tightbond III has a little less power than II but it is more water proof.