What are my options for refinishing these cabinets?
You can refinish them any way you choose.
You can strip, sand, re-stain, re-varnish.
You can prep and paint.
The doors and the face frames appear to be solid wood, (a least the rails and styles) the side panel is thin ply or press-board with a very thin veneer on it. (sand very lightly if re-staining, test in an inconspicuous place inside the cabinet)
If you want to paint them then give them good washing. You will want to sand them so you get good paint adhesion, or alternatively you could use a good bonding primer.
Paint them with a good quality cabinet paint.