The stain needs to be top-coated unless it is a 1 step poly/stain combo which I do not care for.
I would stain with an oil penetrating stain first then top coat with poly. There are many other stain types avaliable but prefer the oil pentrating.

Definitely apply a finish coat. It will seal against moisture, which is the enemy of wood. Todays woods are softer and from fast regrowth forestation. they are much much more absorbent than the old woods and hardwoods.
Like toddinmn, I like the oil penetrating stains, also.

I have had good luck with the water based stains but they certainly don't work as well as the oil based ones.