Pick the end station, then the train
Hotel in Namba or Shinsaibashi: Nankai Rapi:t to Namba. The limited-express ticket is extra — check that day's notice. Hotel in Umeda, or a shinkansen connection: JR Haruka to Tennoji or Osaka Station. The two supplements are not interchangeable.
What ICOCA pays, and what it does not
ICOCA and PiTaPa tap Metro, JR local trains and most private-rail local trains. Haruka and Rapi:t limited-express tickets are extra. An Osaka Metro day pass is Metro only — not JR, Nankai, Hankyu or Kintetsu.
The airport bus is a third ticket
The airport bus does not take ICOCA or a Metro day pass. Consider it for large luggage when the hotel sits on a bus stop. Stops and times follow that day's notice. Do not assume a bus ticket can be reused on Haruka.