Shibuya to Kyoto on shinkansen

I'm looking at a JR map right now (I have a rail pass). If I want to go from Shibuya to Kyoto, what is the best way to do that? It looks like I would take the shibuya yamanote line to shinagawa where I could then get on the tokaido line. Is this right? how do I do this?
AND could someone tell me how I can reserve my seats shortly before leaving.
thanks!

Yes that is correct, take the Yamanote Line to Shinagawa Station, and take the Tokaido Shinkansen (not to be confused with the regular Tokaido Line is a regular line train).

You can make seat reservations at any JR station from time of departure up to one month before travel.

when i reserve my seats on the hikari, which seat should I get for me and my travel partner that is best to see mt fuji as we travel to kyoto from kyoto?

You should head for the seats at the right in the direction of the train.

that much is obvious...
when i reserve a seat in advance though, i dont know which ones are on the right? a-b-c-d-?
is hikari the same kind of train as nozomi? in that case i will reserve seat E

when we reserved our tickets we asked the staff to place us on the Mt Fuji side: worked every time.