Hakone to Kyoto trains

Hi! We are a group of 12 travelers going from Hakone to Kyoto.
I know we have to take 3 trains Gora-Hakone Yumoto-Odawara-Kyoto (and we will not have the Hakone pass). This means we have to buy at the counter in the stations (or online) each ticket separately? We will travel in mid of june. It is best to buy the tickets in advance online? What if we do not arrive on time for one of these 3 trains and we have to take the next one, would that be problematic in terms of changing the train (and the tickets if so)?
Thank you.

The trains in Hakone can be paid with either IC card (such as Suica, Pasmo, Icoca, etc.) or with paper tickets.

The tickets for the shinkansen from Odawara to Kyoto can be purchased in various ways. Advance purchase is possible and recommended for reserved seating. Your purchase options are explained here:
https://www.japan-guide.com/e/e2018.html#ticket
(Stay away from 3rd party ticket websites. They charge 10+ percent service fees)

What if we do not arrive on time for one of these 3 trains and we have to take the next one, would that be problematic in terms of changing the train (and the tickets if so)?

Reservations are possible only for the shinkansen part, so this question only affects the section from Odawara to Kyoto. If you used e-tickets (smartEX), you can modify your reservations online quite easily. If you used paper tickets, then you will lose your seat reservations, but you are allowed to ride later trains on the same day in the non-reserved section.

From Gora, there is a direct bus to Odawara that is an option for some. I have also stayed at a hotel that offered a shuttle to Odawara which was useful, but depends on the hotel.