What is the simplest way to completely protect wood from water and grime?
Polyurethane seems good, but applying it properly is complicated, with a coat-sand-coat-sand-coat process. Latex paint seems OK for water, but it doesn’t seem to clean well when subjected to grime or other schmutz. (Maybe I need a better variety?)
Is there something effective and cleanable that’s simple to apply, preferably one or two coats without sanding?
That’s quite a few requirements! I let really thin epoxy soak into the bottom of my carport posts and let it cure for a week. Totally waterproof, but had to sand before priming and painting. It also tends to yellow over time. I coat my teak outdoor table with few coats of spar urethane every few years, but it will tend to fade and crack in direct sun, so i still cover it. If you apply urethane after dry to touch but not overnight you can get a few coats done in a day without sanding between.
What kind of longevity are you looking for?
I’ve edited the initial post to use the term “grime” rather than mud, since that more accurately represents the situation I’m thinking of.
That depends. How long do you want the new metal shop tables’ legs to withstand all the cutting fluid and oil and metal dust that get sprayed on them? Because that’s my immediate application. (Though I would like to know for later personal projects too.)
I’m a fan of a hard wax oil like Osmo. It designed for hardwood floors so it quite good at what you describe. It’s very easy to repair if you do get any damage such as scratches or abrasions.
I’m trying a marine spar varnish on a planter I am making. Maybe something designed for use on a boat would be good at resisting grime?
For my shop surfaces at home, I use two coats of Osmo, and then apply paste wax. (No sanding necessary.) The main reason is to prevent wood glue from adhering, but water will bead up on it, makes it easy to wipe down. Also, dead simple to maintain as the paste wax is super easy to apply - just buff on/off.
If you want to go the poly route but don’t want to brush, there are lots of spray options or get the wiping polyurethane. You’ll need to do several coats, but it’ll get you there.
Echoing @atwatsoniii .
Spar urethane. It comes in spray bottles and cans for wipe on (or custom spray) applications. It is the kind of stuff used on some boats to protect and seal from water.
I’ve used it on bath trays and little shelves on the outside of apartment buildings. 2 years easily no visible wear or damage.
Oh… It’s also got UV protection
10/10 recommended.
Sanding between coats is recommended only for a smoother finish, or if you let it dry too long. It’ll need some stuff to bind to. I believe if you do the second coat between 4-8 hours it doesn’t require sanding between. Read the can to be completely sure.
Why not use metal for the metal shop tables?
Because that will be moderately more expensive, and the pool of people with the expertise needed that I can call upon to build them is much smaller. Some things will need to be made from steel; I will have any welding volunteers work on them.
Ah. I’d just use ground-contact treated 4x4 or 6x6 for the legs and expect them to “patina” with use. Or just pre-emptively soak everything in machine oil 
I was planning to have someone here make the tables. That mostly rules out treated lumber, because 1) it’s risky to cut on the SawStop due to its intrinsic moisture content, and 2) we strongly discourage using treated lumber here, because of the noxiousness of the dust produced.