I wouldn't worry too much about them making it across the country undamaged. Mine made it to Kansas City without any drama. They're very well packed.
As far as finishing goes... I wasn't thrilled with how mine turned out when I stained them. That's on me, though, since I should have done more prep work. It's absolutely possible (and easy with some planning) to get the plywood these cabinets are made out of to look great. I'd get a couple pieces of baltic birch ply and play around with different treatments to see what you like best. Of course baltic birch ply is crazy expensive right now, so...