Even though they are old, the cabinet sizes should still be standard, so you shouldn't have an issue if using the same footprint, although if it's an L shaped you might run into issues with corner pieces. Then just make sure the cabinet you get has proper trim pieces to cover any gaps.
If it's 50 years old, I would turn off the gas myself to the area, but have a plumber come in to see if any of the connections need updating. More than likely they'd replace some piping with the yellow flex pipes.
Are the cabinets not able to be refinished? Our cabinets are at least 30 years old, and our previous owner took the blah stained color and painted it white, replacing hardware, countertops, sink, appliances, etc. Looks brand new. From what friends said unless you are changing the layout it should be rare to have to replace the actual support structure (the box).
But my experience is really limited, mostly from a recent bathroom / laundry room remodel.