This is probably more appropriate for the woodworking group, 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.