The greatest advantage of the Metro is that it goes more places in central Tokyo than the JR commuter lines, such the Yamanote or the Chuo or the Sobu.
I don't know where you're finding so many stairs on the Metro. My impression is that the Metro is mostly served by escalators, some of them very long, much more so than the JR stations, many of which still have stairs only, although I'm finding more and more elevators.
My advice would be to get a Suica or Pasmo card and simply use either the Metro, the JR, or the private commuter lines (Toyoko, Keio, Seibu, etc.) depending on which goes closest to your destination.