Stains are not a protective finish.

You can really use any type of wood finish to protect your investment. I use what ever is left over from a job most times. If you are going to buy something. Two I would recommend would be 4lb cut Shellac or a water based polyurethane floor finish. Both dry very fast and provide good protection.

A note.....New basswood boards are like a sponge. apply a light first coat to seal the wood, 2nd,3rd coat is to build up the finish film