Travel from Tokyo to Gora

Hello, can you please advise the most efficient way to travel from Tokyo (near Shinjuku station) to Gora station in Hakone area...And, most importantly how/when to get tickets for the train or bus?

Same question for getting from Gora to Kyoto Station. What is most efficient and how/when do I get tickets?

We are traveling in March.

Thank you!

Shinjuku to Hakone Yumoto by Odakyu line. Either Express train (no surcharge) or Romance car (surcharge needed and I think reservation needed)
Depending on time of the day, eh if you go in the morning if a weekday, normal express train should be fine. Most people go in the other direction so those express trains arenft too full. Plus they start at Shinjuku station so you just need to line up a bit ahead and have a seat guaranteed.

Gora to Kyoto:
gora - Hakone Yumoto
Hakone Yumoto - Odawara by Odakyu line
Odawara - Kyoto by Shinkansen

If youfll ask about travel pass the Odakyu pass for Hakone LOCALLY can be useful if you do gthe looph but the pass from Shinjuku is not paying off because you donft go back to Shinjuku

Thank you for this information. Alas we are traveling on a Saturday.

If I am also getting a JR Rail pass, do you agree it would make sense to do this:

Arriving...
JR Rail: Shinjuku-Odawara
Odakyu Line: Odawara to Hakone Yumoto to Gora (is there a single train for this or is it a transfer? I cannot tell)

Leaving...
Odakyu Line: Gora to Hakone Yumoto to Odawara
JR Rail: Odawara to Kyoto

Thank you!

Calculate well if JRP pays off. It is rather unlikely unless you have a far flung rapid trip planned.
But yes, if you have JR pass youfd need to do JR from Shinjuku to Odawara. Either Shinjuku - Shinagawa and Shinkansen from there or normal Tokaido line. From Shinjuku Odakyu line would be more comfortable.

Hakone Yumoto to Gora is a small train. I donft think it goes anywhere outside these stations so you always need to change at Hakone Yumoto.
If you need to change at Odawara to Hakone Yumoto depends on the train. If JR you must change. If Odakyu some Romance cars go all the way to Hakone. Express trains donft.

From shinjuku to Gora station = 1680 yen
By odakyu railway and hakone tozan railway
You can buy odakyu rail 1 day pass=2000 yen
You can buy hakone ashinoko ticket valid oda kyu rail ,hakone tozan rail ,hakone tozan bus