A standard approach to sealing is polyurethane, either brush on, rub on or spray on. If the old finish is pretty solid, a light sanding may do. If it is not adhering well or where the piece is worn and stained, a more thorough sanding is needed. In all cases, you need to wipe off all dust, preferably with a tack cloth before finishing. Wiping down with mineral spirits also helps clean before finishing.
A dust mask is always a good idea when sanding, especially if there is a chance that mold is present.
A much harder finish is marine or spar finish. While originally varnish, it is now available in a urethane formula as well.
These types are specificly formulated to hold up better in wet environments.
For almost all types of finish, two or more coats are needed for a durable protection.
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