By "Early 60s" are you talking about a dryer with the perforated drum back or a dryer with a solid bulkhead with an inlet grill for the hot air on the left side and another grill on the right side for exhaust? The design changed about 1964 or 65.
You will first connect it to electricity and see if it starts. Have the lower panel open and see if the igniter comes on and glows until it is yellow or, if it still has the original spark igniter listen for a loud racket. If that works, and you have the pieces needed to connect it to gas, I would say try it. Depending on how it has been maintained, it probably needs to be disassembled and cleaned and the tub bearing lubed, if it is a perforated tub back machine. While the tub is out, you will cut some felt strips to glue on the solid bulkhead behind the drum in a crescent shape to the right, above and below the air inlet and to the left, above and below the exhaust port. This helps keep the air from travelling behind the drum and forces more of it through the rear of the drum into the load for greater efficiency. I hope your dryer has the 37,000 BTU burner. Those are amazingly fast dryers. Write back for what you need to do for a solid bulkhead drum