Some furniture will finish and look very good with either. Both can provide degrees of sheen. For waterbased polyurethane, it works well sprayed, but can also be wiped on. It's available in a gloss, and satin, or sometimes called semi-gloss.
For oil base polyurethane, I don't usually spray, but rather wipe on. It can also be brushed on. It's also available in different sheens. It can be thinned for a wipe on as is, or an amount of Tung or BLO could be added for a wiping finish. It doesn't necessarily have to be done to look plasticky. It will produce a very durable finish.
Straight oil base varnishes can be used the same way.
Your other choices could include spraying lacquer. You also might consider shellac.
For other than a film finish, you could use just an oil finish.
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