That's going to be somewhat of results driven issue. To know what you might best use you will have to know where you want to end up.
There are two kinds of Walnut. English walnut (my favorite) and American black walnut. They don't look the same.
You could finish with any polyurethane (oil or water base) I like the oil based polyurethane because it's less finiky about whether your sand paper had stearates in it. A shellac might be nice. Some would oil it first and then shellac it with the end result of causing the grain to be highlited. Some might use an oil and polish it with a wax and a buffing wheel while others might just use tung oil. Other folks might de-wax their shellac and then apply that over an oil base and then apply a polyurethane on top as a water resistent sealer.
Really, the sky is the limit.
If you have little finishing backgroud you might stick with oil based polyurethane and a lamb's wool applicatior.
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