It's probably varnish, as you suspect. So, it's oil based, being of
that vintage. Using any waterbased product over it will likely not be
satisfactory.
I would remove the doors/drawers, take them out of the kitchen
(outside?) and sand them to remove the varnish coat. If you are OK
with present stain color, then recoat with an oil based polyurethane.
If you want a different shade or color, You may have to resort to
stripping it all, then sanding.
Even if you apply an oil based paint, you will need to sand away the
varnish coat first.
Whatever you decide, the face frames will have to have the same
treatment, of course.
good luck!!
Gene

On Mar 17, 1:31 pm, "Eigenvector" wrote:
This is probably more appropriate for thewoodworkinggroup, but I'll cast
my line out and see what happens.

The finish on my cabinets is a badly worn varnish. I say varnish because
its a flaky yellowish crystaline substance from the 1960's over plywood.
After removing the varnish from the cabinet boards I notice that the cabinet
isn't a natural wood color so I'm assuming it was stained. My question is
what kind of a finish would be best for wood like this?

It's not like its raw plywood or something, it has a nice hard smooth finish
so being unfamiliar with plywood construction I can only assume its a
hardwood laminate or similar material.

I guess my question is, if I restain it, do I need to apply varnish to seal
or are there better alternatives? What if I like the original color and
simply want to seal/complete the finish from weathering (hands, kitchen
smoke, traffic, etc..)

I'm used to working with linseed oil, I use it to refinish my gunstocks, but
something tells me I don't want something that flammable in the kitchen.