There is more than a few schools of thought about this. Some feel that it's best to paint all wood surfaces to reduce the amount of hiding places for mites, and as long as the paint is not peeling it's great. Some think that untreated wood is the safest. Some like a washable surface and put vinyl up on the wall or some other simular material.
I'm using a food grade Diatomaceous Earth whitewash in our playhouse coop (pest deterrent). I apply the whitewash to all the roosts (helps dry the poo quicker).
Two or three coats of MinWax polyurethane is by far the best interior finish I've ever used.
Poly gives an extremely durable hard shell finish that's smooth and easily cleaned. And it's waterproof plus it gives a nice golden glow when applied to bare wood.
Use the exterior or spar type of course...