It is difficult to say without knowing your exact schedule and without knowing where you head afterwards.If you head somewhere else afterwards, a Japan Rail Pass in combination with the Koyasan World Heritage Ticket might be best:
http://www.japan-guide.com/e/e2358_012.html
If you don't use a Japan Rail Pass, a Kansai Thru Pass might be the better solution than a Koyasan World Heritage Ticket:
http://www.japan-guide.com/e/e2357_005.html
Lastly, you might want to look into the Kintetsu Rail Pass:
http://www.japan-guide.com/e/e2357_006.html