Killz is a great product, but only a primer. I would use killz, a high quality exterior window/door/bathroom caulk like GE and a couple layers of high gloss oil based paint. Sand the wood very, very smooth to get a fine finish so the paint lays down flat and the end result has no burs or roughness. This way when you drag a towel across the wood it doesn't snag and instead the surface is like glass.
As always, success with anything like this is 90% prep and 10% finish.