“Kills” brand paint and primer is Anti microbial. then water sealer paint on top or second layer of kills in a pinch.
Kilz. And yeah , just paint it. Kilz isnt necessary but I'd use a quality paint , either a Sherwin Williams product or Ben Moore. I've been using alot of Ben Moore ' Command' commercially lately and i really like it. It can be used inside or out. Don't use exterior paint indoors, sounds good, but not a good idea. So an exterior/interior is your next best bet. 1 coat of primer, 2 coats of finish. There are packets of antimicrobial additives at most paint stores. They're meant to be shook in 1 gallon paint cans. With these, any paint can be "antimicrobial " I wouldn't worry about that personally, but I would use the highest sheen (Gloss) for my finish coats as it's the easiest to keep clean, and the higher the sheen, the harder the paint is.
Not sure why everyone is concerned with mold if it's painted, bathrooms vented/painted correctly dont mold.