How far ahead to buy train tickets?

We plan to travel by train from Nara to Takayama and a few days later back from Takayama to Kyoto.

I have found the following train connections using Hyperdia

Saturday Oct 27. 9:39 NARA to KYOTO JR Nara Line, 10:46 KYOTO to NAGOYA SHINKANSEN NOZOMI 8, 12:03 NAGOYA to TAKAYAMA LTD.EXP (WIDEVIEW) HIDA 7

Tuesday Oct 30 09:42 TAKAYAMA to NAGOYA LTD.EXP (WIDEVIEW) HIDA 6, 12:34 NAGOYA to KYOTO SHINKANSEN NOZOMI 21

We fly into Japan and go directly to Nara on Wednesday Oct 24. Should we buy the train tickets before we arrive in Japan (and how do we do that) or will it be OK to buy them on Thursday Oct 25 at Nara JR station?

It is currently not possible to make train reservations from outside of Japan. I don't think you should have problems making seat reservations for the mentioned trains on October 25.

Some of those trains are not possible to reserve before hand, ie Kyoto to Nara via JR is all unreserved seating commuter trains. Kyoto and Nagoya are pretty close and fast by Shinkansen, so even by nonreserve seat it should be just fine.

Every time I've left Takayama the last few years I've had to go "free-seats," as all the reserved seats were taken. One time the WideView was almost a commuter train with people standing in the aisles. I don't know why it got filled up toward Nagoya, but if you want to be sure of seats, make your return seat reservations for Nagoya on the WideView early.