Dad pretty much furnished our whole house with "finds" like this when we were growing up. Of course, back then you could walk around the dump and find all sorts of cool stuff. Some of them were absolutely beautiful once you stripped off all the spray paint or whatever other glop someone had applied. I think that's probably where I developed my abiding love of nicely figured wood.
Anyway, the stuff he swore by was
Formby's . It always seemed to work for him.
ALWAYS WEAR PLAYTEX GLOVES AND SAFETY GLASSES. And to preserve that veneer I would remove the Formby's with an old credit card scraper and then rub it down with a wet coat and some "0000" steel wool. This will leave a really nice surface, ready for your choice of finishes. Formby's also makes a Lemon Tung Oil, which is basically just a liquid you sipe on real wet, let it sit ten minutes and wipe it off. Let it dry a couple of days and repeat. Let it dry at least a week and repeat again.
Nowadays I am partial to an old finish I discovered in an antique woodshop text. Equal parts of boiled linseed oil, mineral spirits, and varnish. I usually mix it in batches of one pint of each. Shelf life is about six - nine months. It is also a wipe-on finish. You wipe it on and let it dry for ten minutes then wipe it off with a clean rag. Two days later repeat the process, except let it sit on there for about 15 minutes. And then one last coat after one week, letting it sit for about 15 - 20 minutes, but wipe it off before it gets tacky.
PLEASE REMEMBER THAT ALL OF THESE CHEMICALS ARE CAPABLE OF SPONTANEOUS COMBUSTION. Lay the rags out flat on some outdoor surface to dry.
NEVER PUT THEM IN THE TRASH UNTIL THEY ARE COMPLETELY DRY. I go so far as to keep a 10 gallon galvanized trash can with lid outside to store them until I put them out at the curb.
Another book I have recommends an old Shaker finish, just plain old linseed oil. Wipe it on and let it dry on the piece. Apply one coat daily for a week. Then apply one coat weekly for a month. Then apply one coat monthly for a year. Then just refresh the oil once a year. That's ok for someone who's got the piece in their house, but not so great for someone selling pieces.
I have also used Carver Trip Water Based Polyurethane with reasonable results. Apply one coat and let dry two days. Scrub down with "0000" steel wool and then wipe clean with a tack cloth (available at HD or Lowe's). Apply a second coat and that's it, you're done. Although you could do a third if you wish. I would.