Which JR rail pass query?

Hi, total Japan travel novices so hoping some kind soul can make sure we book the right JR rail pass. We're flying into Osaka on 3rd April, then getting the train to Kyoto the same day, where we stay for 6 nights. We will probably be mostly in and around Kyoto itself. On 9th April we move to Okayama as a base for 4 nights, with days out from there, so quite a bit of train use I expect. On 13th April we train to Kanazawa, again as a base for 4 days + with day trips out, possibly using trains. On 17th April to travel by train to Osaka for the last 4 nights of our holiday. During these 4 nights, again day trips out planned, including a night on Mount Koya. We fly out of Osaka on 21st April. Which JR rail pass will we need to get to ensure we cover what we need but without over paying?
Many thanks!
Kind regards, Nigel

It is a little difficult to say without knowing what side trips you will be making (especially from yur Okayama and Kanazawa bases).

But the following pass looks to be quite a good match except that its coverage period is only 7 days:
https://www.japan-guide.com/e/e2361_kansai_hokuriku.html

As Uji wrote it depends on your side trips, but I would consider a mix of following passes.

Kansai Hiroshima Area Pass for your Osaka to Okayama and then to Kanazawa trip (as far as Tsuruga).

https://www.westjr.co.jp/global/en/ticket/pass/kansai_hiroshima/

Hokuriku Area Pass for your Tsuruga to Kanazawa and "side trips".

For your last Kanazawa day (to Osaka) you may better consider normal ticket to Osaka or the combination of normal ticket to Tsuruga and then Kansai Wide Area Pass or Kansai Area Pass.

https://www.westjr.co.jp/global/en/ticket/pass/kansai_wide/
https://www.westjr.co.jp/global/en/ticket/pass/kansai/

JR does not go to Koyasan so you need some non-JR pass such as Kansai Thru Pass (or individual tickets).

https://www.surutto.com/tickets/kansai_thru_english.html

I'd also say some regional passes will likely serve you better. But you didn't go fully into detail. The JR Kansai Wide Pass goes up to Kurashiki, and might suit you well. You can also use it to go into Kagawa, and seeing Kotohira and Takamatsu is well worth it - the Ritsurin Garden is one of Japan's best.
https://goo.gl/9WXVpM

For seeing Koyasan, the World Heritage ticket is also another option to consider.
https://www.japan-guide.com/e/e2358_012.html
One night there is enough though, unless you want to do a lot of hiking in the region. No matter what though, do not miss Okunoin - it's one of the most surreal places in Japan.
https://youtu.be/uquvCbWANBo

But if you want to see the place at night as well, be sure to pick a place to stay with no curfew. I learned that too late, and wish I knew before.