I think the first station was 640 AM. It was started by Rose Poly (now Rose Hulman) in the late 20s and became WBOW when it went commercial. 640 has been dark since 2001. The longest continuously operating AM is probably 1480 WPFR (formerly WTHI), but I don't know the first air date of 1480.
On FM, I think WTHI-FM is the longest continuously operating station. Both WTHI-FM and rimshot WWBL have been continuously operating since 1948, not sure which one was actually "first."
WTHI-TV was the first TV station, signing on in '53 or '54 from the 500' tower on Ohio St (then shared with WTHI-FM, now just the FM). WTWO didn't sign on for several more years.