Best type of caulking for waterproofing plywood?

I'm building a darkroom photo sink from 3/4 plywood. We need to caulk the seams after two coats of marine primer, followed by two topcoats of marine, then spar varnish.

Any thoughts on type of caulking to use? Also, I saw mention somewhere of a type of caulk that can be painted while it cures? Interested to know if anyone knows about that, too.

Thanks for your kind replies!