At first glance, flying an airplane built before 1970 isn’t a big deal. The FAA doesn’t get too excited about it in the regs. If the airplane of choice has a tailwheel, FAR Part 61.31(i) requires a tailwheel endorsement from a CFI if you don’t already have one. Otherwise, the regs are silent.
There’s no type rating required (we’re talking about piston-engine airplanes weighing less than 12,500 pounds.) You can legally hop into a World War I era Curtiss JN-4 Jenny and fly it.