Shinkansen prices from Tokyo to Kyoto

Hello,
I haven�ft been to Japan for a few years and I use to by Jr pass, but now it�fs no longer around.
This time I�fll bring a family of 4 to this trip.

I�fm planning to go from Tokyo to Kyoto, then Kyoto to Nagoya. Finally Nagoya to Tokyo. Planning to have one day trips in Nagoya and Kyoto.
I found a site called klook. It looks a bit cheaper than what google map is giving me.

Would anyone have any experience with klook on Shinkansen? Or if you have any discount ideas?

If not, I was thinking of buying the ticket from the JR machine when I arrive.

Thank you in advance!

The basics about buying shinkansen tickets is explained below. I recommend to limit yourself to official JR channels unless you really need your ticket before coming to Japan and can't get them through the JR sites: https://www.japan-guide.com/e/e2018.html#ticket

And basics about using trains in general:
https://www.japan-guide.com/e/e2016.html

I'm not sure what you mean by the pass not being around. The full JR Rail Pass?
It's still around, but with their current prices, it's pretty much a waste of money for nearly everyone.

Klook or ticket machine is fine. Pick whichever.

Klook doesn't offer every train available.

Advance purchase tickets via SmartEx website offers a saving.
I see no reason to use a third-party (like Klook) for tickets - I doubt you get the same protections and ability to fix things when you need changes or when things go wrong. Use the official JR options, either online for booking or in person for tickets.

Also, most third-party sites, like Klook, charge at least 10% additional.

Thank you all for the tips. I will stick with booking on jr machine when I arrive.