The IRT is on Broadway there are local stops at 110th, 116th and 125th Street is an express stop if you are headed to the northern part of the campus. 96th Street is an express stop where you can change to the local. If you take the B or C trains you will not end up on the Campus if you are trying to get to the campus near Morningside Dr, Amsterdam Ave and Broadway or Claremont Ave. you will have to climb the stairs from Harlem and Morningside Avenue up to Morningside Drive.
I would stick to the IRT on Broadway. Do remember that two the stations for Columbia are local stops. So you have to be on a local train. Express stops where you can switch to a local train are 59th, 72nd and 96th.
Coulumbia's medical school is at the 168th street stop at Presbyterian Hospital on the IRT line too.