Ideas for box ends and what style of edge to do

Edge treatments are limited only by your imagination. Your idea is a good one, but don’t be afraid to experiment with routing over joints… sometimes you get a really interesting look.

-- Charlie M. "Woodworking - patience = firewood"

IMHO, I would not do anything to dramatic the beauty here is the joinery. I have done a simple roundover or chamfer and that seemed enough. Again beauty is in the eye of the beholder so what ever you do, if you like it that’s what matters.

-- Have thy tools ready. God will find thee work.