Stained would hold up better than painted

Every single bench top, painted or stained, needs a cushion in a "bullet poof," fabric. Or plan a lot of annual maintenance in either finish. Best is a faux leather two inch firm foam cushion, custom made to your specs in an upholstery shop. Wipe up and done. For basically.......forever.

These are package depositories, back pack dumps, .......: ) not just coat/snow pant drips

You might research a poly finish used for bar tops. I used it in the laundry of my previous house to protect the counter.

I have Butcher Block counter tops in a ski condo and I put Watco sealer on them. That is just about bullet proof. It is clear so it shouldn't change your stain much.

https://www.amazon.com/Watco-241758-Butcher-Block-Finish/dp/B000VITOT4?th=1

I will look into poly finishes. Is there any particular type of paint that would hold up best on the built-in shelves?

if are worried about water, you can also look at marine spar varnish and marine exterior waterlox. We have used both on exterior wood surfaces where they get actual rain and occasional snow.

I like a rimmed rubber boot mat for muddy or wet boots and shoes, and I also put a boot mat under wet/drippy jackets and rain coats. It looks like there is a shorter bench on the opposite wall for sitting to remove boots or shoes. During winter I have an absorbent machine-washable rug on the floor and a roll of paper towels. Drip happens.

KitchenVisions designed and supplied this mudroom. Yes, the bench is waterproof and coated with a Spar varnish. It doesn’t need a cushion. The bigger issue would be scratches if people were to stand on it with grit on their shoes and boots from outside.

another recommendation for either exterior spar varnish (I have it on a bathroom counter) or marine water lox (I have this pine kitchen floor). both are holding up really well.

How big is your closet? Would the kids have to line up and wait their turn to get in there and sit down on the bench? Kids are not tall, cubbies near the ceiling would be out of their reach. Snowy Coats need to drip onto a water friendly floor or a boot tray, not a bench.

I agree with Shady Willow Farm.. I always laugh at the pretty pictures that show two coats and two pairs of shoes in the little mudroom area. Puleeze! This is how it will really look...

No one will have space to sit on the bench with backpacks etc on there.

Will you have space on both sides as shown in the picture above? I would strongly encourage a study Locker style (with hooks on the sides to hold more stuff), however I would leave the bottoms (under the 'bench' shelf) open to the floor, add a single metal basket for shoes (Ikea has them for their PAX cabinetry) and put removable boot trays under. You could have the supports taper off to the wall similar to corbels on a countertop. Have the unit be the same depth across so the littles can reach their hooks. No one will be able to sit on that bench - have a separate one on the end or other side.

If you have forced air heating, a vent under the bench would help with drying. I would move your hooks down for the little ones and put adjustable shelves just above. As the kids grow and their coats get taller you can move the shelves and hooks up. DO use storage bins for off-season stuff and sports equipment.

Open bottom like this for drying shoes. Maybe a basket directly under the shelf for corralling summer shoes.

We have a floor to ceiling storage unit for all our mudroom stuff. Shoes are usually dried on the boot mat first then into the baskets (one for each family member). You will need to reconfigure as the kids get older, so think ahead to what they will need and make the cabinetry flexible and changeable. We struggle with wet, stinky hockey gear that needs to be dried/aired out in the house (so it doesn't freeze in the garage). Musical instruments? I also left space for staging returns back to the store, keys sunglasses, etc.

As far as the water on the bench top, I have found it to generally wipe up pretty well. Its not usually puddles. most jackets hold the water until it dries. If you are really worried choose a solid surface top like quartz or formica.

The closet is 82" so pretty wide. We'll have shoe baskets underneath the bench as well as a boot tray or two. I don't expect it to look like the staged pictures, but it will certainly look a whole lot nicer than it does now! They normally throw their coats on the floor anyway so I'm not hugely concerned about whether they can reach the hooks well. And we homeschool so no backpacks.