KIX, Kyoto, Koyasan with Icoca and Haruka

Hi guys, this is my first question on this forum. I have found several questions similar to mine, but most of them are very old.

We are planning our three-week itinerary in Japan, starting in KIX, and then:
5 days in Kyoto
2 days in Koyasan
1 day in Osaka
and others...

I'm wondering what would be the best option for getting from KIX to Kyoto and to Koyasan five days later. HARUKA+ICOCA deal would allow us to go to Kyoto on our arrival and we would then have ICOCA prepaid with Y1500. Later on we will probably buy JR Pass for two remaining weeks, but before we do, I would like to make sure.

Can we use ICOCA on Nankai Koya Line Exp. and Nankai Koyasan Cable Car to get from Kyoto to Koyasan? Hyperdia says: KYOTO - OSAKA - SHINIMAMIYA - GOKURAKUBASHI - KOYASAN

Is there better option?

Thanks,
Barret

Alright, it seems that Kansai Thru Pass (Surutto Kansai) is also a good option for travel to/from Koyasan since it covers Nankai Railways and calbecar to Koyasan as well as city buses in Kyoto.

Source: http://www.japan-guide.com/e/e2357_005.html