Here are a few suggestions:
1) Waterlox-- a tung-oil based varnish that does exactly what it's name implies. Cost a lot, but a very, very nice product. Hard to find in "local" stores but easy to find online. Dries slow. Two coats should do you very well. USE SATIN if you don't want it to look plasticky.
2) Spar varnish--- will achieve similar results as the Waterlox, but darker in color (which would look just fine on mesquite). Easy to find: Lowes, Home depot, and can also be bought in aerosol cans. We use the aerosol cans at work for little onesies and twosies. Dries slow, but again, two coats should do you fine, and again, use satin to avoid the shiney plastic look.
3) Precatalyzed lacquer---- Mohawk sells a very nice precat that, if you can find it (Klingspor sells it where I am) it is a good finish. Dries very fast (sandable in 30 minutes normally), but will require 3-4 coats and is a touch less water resistant than the above two. I love precat lacquer. I spray a post-cat version on my pens and absolutely love it.
There are lots of other waterproof (or resistant) finishes out there, like 2-component polyurethanes, gelcoats, and epoxy resins, but the exorbitant cost makes them pointless overkill for most of what we do.