From what I understand, if you are under 40, you should be all set for 60 months from your 1st class , if all you're doing is private pilot (3rd class)flying.

You can use that (first class) certificate as first class or second class for one year. After that it becomes a third class. Under the new rules a third class is good for 60 months (under 40). Take a look at
Medical Certification