I'd use drywall screws. They're easy to drive in
and don't need to be pre-drilled in plywood or joists.
I don't actually use "wood screws" for anything.
If I need small screws I use sheet metal screws.
Better threads that drive better. Wood screws
are designed for hand drilling and hand screwing.

If you're going through oak you'll need to pre-drill
countersunk holes... and presumably be certain
that you'll never want to have that oak showing
again.