Ok, no oversized luggage. Is there a benefit if I bought in advance, like a discount?

https://smart-ex.jp/en/product/

We were visiting Japan 2 weeks back. I would suggest buy in advance. Save time at the station. There can be long queues as well to buy tickets. Online interface to buy tickets does not accept visa credit card. Only Amex and Mastcard. On the online website, a QR code can be generated to pick physical tickets at a vending machine at the station.

I often go to Osaka from Tokyo for business trip. I always make reservation one day before the day I get on. So it's enough make reservation after arriving to Japan.

My husband likes non-reserved seat of Shinkansen. He always doesn't book the ticket.

If you get on Shinkansen from Kyoto to Tokyo on Sunday afternoon, you would be better make a reservation earlier. Many people live in Tokyo area travel Kyoto on weekends.

I make reservations on the website of JR Tokai Tours when I go to Kyoto with my friends. In this case I can't change the time of Shinkansen, but much cheaper. For example if I go to Kyoto the day after tomorrow, stay one night in Kyoto, then come back to Tokyo, the cost is 40540 yen (make reservations Shinkansen and a hotel 12600 yen). But it become 29190 yen on the JR Tokai Website (non changeable Shinkansen and the same hotel).

Thank you @Michan and @Raman G - I will be traveling on a weekday June 5 and return June 6 Tokyo/Kyoto route. I don't have a Mastercard so this will not be helpful for me to make advance reservation online. It sounds like I need to do it when I get to Japan. I will be alighting at Shinagawa Station so I'll purchase it there. @Michan - I will check out the website you mentioned. I have not yet decided if I want reserved seats or not. Is first week of June already crowded? I realize that is not a holiday week in Japan. Thanks.

It's normal travel in that timeline. You'd have no problem buying the most frequent and fastest Nozomi Shinkansen train tickets after arriving in Japan. Note that it can be purchased at JR stations either via automated vending machines or at manned counters - longer lines for latter in major stations such as Tokyo, Shinjuku though. No need to travel to Tokyo or Shinagawa station for such.

Each JR Nozomi Shinkansen train has about 1,300 seats in 16 cars, excl 3 green cars. it ops once every 10-15 min as mentioned.

https://www.japan-guide.com/e/e2018_tokaido.html

With ten+ trains per hour, you will not need to book in advance. The ticket machines take around two minutes to book a reserved seat if you want to ensure a space to sit, but the non-reserved cars at likely to have space for a non-busy period like June .

Thank you DLi_hk and @JapanCustomTours. Is there a JR station at Shinagawa Station? That will be the closest station to my hotel at arrival in Japan. Thanks.

Of course there is.

Most local business hotels are around the JR Shinagawa station, where it's closest to HND with 2 domestic terminals in less than 20 min by Keikyu commuter trains.

https://www.jreast.co.jp/e/stations/e788.html