I'd take a belt sander to it and then Minwax the top, but that's me. I think poly would look silly even if I went with satin. It's kinda like polishing a turd. I do understand what you're after, trying to stop water marks and rings. I think I'd just accept that and use placemats. Some rings add character.
To keep "the look" through the whole table, you'd have to refinish and poly the whole thing. If it actually is pine, and it's probably soft maple or something of the like (who makes tables out of pine?), it's just a tough project, period.
Even tougher to assess the finish without seeing the piece, ya know?