Polyurethane varnish is one of the best things for this as long as you don't mind the colour it imparts. Poly is cheap but both highly scratch and water resistant, and can be a doddle to apply to a high standard now that wiping it on has been widely popularised so that there's lots of good advice out there on how to do it.
If you don't like the look of a built film finish you can apply it more thinly (e.g. three thinned coats with excess wiped away) but it's the same with all finishes, thin = less protection.
Is there any end grain exposed that might get wet during normal use? That's the surface to pay most attention to as it's most absorbent and also the hardest to seal. You could seal this thoroughly with epoxy prior to applying the varnish (or another finish) if you want to truly waterproof it.