Your FAA pilot certificates never expire. Certain other certificates expire, but can be renewed. In your case, your pilot certificate is good for life - but you need to reestablish currency.
You NO LONGER NEED A MEDICAL for most Private Pilot flying. You can fly VFR or IFR s a Private Pilot without an FAA medical. Go to the FAA web site an read about BasicMed.
https://www.faa.gov/licenses_certificates/airmen_certification/basic_med/
BasicMed let’s you simply go to your personal doctor and he attests that you are in generally good health. Most Private Pilots no longer need an FAA Medical. Just BasicMed.
Then you need a Bi-Annual Flight Review (BFR). A BFR is required for all pilots to maintain or reestablish currency every 2 years. Commercial pilots can use FAA recognized recurrency training (every year, or every 6 months FAR 135 or FAR 121, or under an AQP program, the interval established by the airline).
In your case, I would recommend more than a simple BFR. If you plan to rent an aircraft, it is unlikely they will let you do it simply with a BFR. Since the national airspace has significantly changed over the last 50 years, you will likely want to spend some time with a CFI in a classroom or briefing room in addition to the cockpit...
Having said all of that, aerodynamics have not changed, and an airplane is an airplane. Many, many of the private aircraft out there are 40+ years old, so you can likely find something to rent that will come back to you... like riding a bike.
Blue Skies, in your most worthy pursuit!