Buy on spot thru ticket machine.
Kodama class "stop every station" and let Nozomi and Hikari class go thru. Journey about 2 hrs 30 minute.

Don't forget buy Bendo at Mishima Station before board the train.

No need reserved. Just buy Shinkansen Ticket on the spot at Mishima Station.

Fuji Excursion Limited Express can be purchased at JR Ticket Office in Shinjuku Station or JR Ticket Machine.

Japanese train will have 2 ticket. One is for the train, another is for the seat.  Remember, passing autogate by using train ticket only, don't put seat ticket inside machine.

Normally reserved seat in advance are only for those travel during Golden Week or wanted to ride those super rare sightseeing train.
Reserved seat in advance are advance tight your schedule in that particle timing which is very stupid specially Tokaido Shinkansen got 90 train schedule running from Tokyo to Fukuoka vice versa daily. As long no holiday, 100% confirm got seat & train not even 50% full.

If you reserved seat in advance:
From lake Kawaguchiko to Mishima Station bus got any delay. You are fxxx, late 5 minute you are fxxx because Shinkansen are super duper on time. Example 10:30 am train, 10:20am train will be arrived platform & 10:30am sharp door will closed. Japan buses sure will delay because road condition always unpredictable. Seat reservation will making you need to arrived Mishima Station 30-40 minute in advance.  So stupid.......you making your journey from Kawaguchiko to Mishima like Amazing Race for something had 90 schedule train running daily which is every 15 minute will had one train from Tokyo heading Kyoto.

Oh yea, you reserved in advance, you late, you will burn that 16,000 Yen - 20,000 yen Ticket.

Seat reservation can be done even if the train arriving in 5 mins if they still have seats available (which usually have). If not, just reserve the next train and relax at the station by strolling around or browse FB

Example:
It will be Kodama こだま No.25 & Next train will be Kodama こだま No.32.  Normally Kodama こだま are higher frequency to Nagoya Station. From Nagoya Station you can take another Hikari / Nozomi Class to Kyoto Station. 

From Mishima got Kodama Train to Kyoto Station, frequency is about every 1 hour per train compare frequency to Nagoya Station (25 minute per train)
* Mishima Station are not Major Station,  Shinkansen Nozomi & Hikari Class does not stop at Mishima Station.

When you reach the station,  buy the ticket from JR Ticket Office. Once you got the ticket (normally will be the next arrived train). From ticket you got the train no. Info. Seat no. And coach no.

Train no. Info can get from big info monitor similar to airport. Big info monitor will show next train arrived time and which platform.

Example of Shinkansen Ticket.