I have a rental apartment in my home which has cabinets that are about 40 years old.

You can also buy new doors, and veneer for the cases, at Rockler.com.
Much cheaper than new cabinets, but probably more expensive than
refinishing. Amount of time might not be too different, though.
If it's just the finish on your old cabinets that's in rough shape, I'd
sand them all very lightly (try to avoid sanding through the finish
into the wood) and then put a new coat or 2 of polyurethane varnish on
top. As long as you've sanded, poly should stick to most previous
finishes.
In my opinion, white paint would look fine too, unless you have some
really nice-looking wood in your cabinet doors. If the wood is old and
dark, a light-colored paint will brighten up the room, too. You'll
still want to sand before painting.
Shellac will be softened by alcohol (I don't know what "meths" in a
previous post means), but alcohol won't soften varnish (including poly)
or lacquer.
Good luck,
Andy