Transport tangle

Hi. After reading the forum and speaking to other travellers I知 still not able to work out the best (most cost effective) rail ticket for my trip and I知 hoping someone can help.
I am visiting Japan for 9 days in mid-March and my itinerary will be as follows:

Day 1 Arrive Kansai Airport (late night).
Day 2 Osaka
Day 3 Travel to Koyasan, overnight stay.
Day 4 ・7 Kyoto. Intend to do day trips: Arashiyama, Iga-Eno, etc
Day 8 Shinkansen to Tokyo. Overnight stay.
Day 9 Shinkansen back to Osaka. Fly out of KIX (late night)

Baring this in mind, would I be best to get a JR 7 day pass plus 2 day Kansai Thru Pass? Or the JR 7 day pass (this will cover cost of Kyoto ・Tokyo ・Osaka on shinkansen) and buy single tickets as needed? There are so many different options it痴 quite overwhelming.
I don稚 really have solid plans as such, am planning on going with the flow, but would feel better if I have an idea of the best (and cheapest) way to get around.
Thanks in advance!

I recommend a 7-day Japan Rail Pass for the round trip to Tokyo. Koyasan Sabic or Kansai Thru Pass for the trip to Koyasan.