How to buy rail tix Tokyo to Kyoto?

We are 3 adults (1 college student); want to take bullet train from Tokyo to Kyoto on 10/15. Then Kyoto to Osaka for day-trip on 10/16. Then bullet train from Kyoto back to Tokyo on 10/17.
Should we buy rail tickets ahead of time from New York? Where and how? How to get the best fare? Should we reserve seats ahead now? Are there discounted student fares?

We will also need Keisei Skyliner train from Narita to Keisei Ueno station in Tokyo (to hotel). Any combo rail/train/subway packages with Kyoto train? And any additional discounts or passes for local subway within Tokyo (6 days)? Thank you.

Should we buy rail tickets ahead of time from New York?

Yes, I recommend to use a 7-day Japan Rail Pass, unless you are on a tight budget, in which case I recommend to travel by nigth bus.

Basic information:
http://www.japan-guide.com/e/e2363.html

Japan Rail Pass:
http://www.japan-guide.com/e/e2361.html

Night bus:
http://www.123bus.net/index.html?agencyCode=4268

How to travel between Narita Airport and Tokyo:
http://www.japan-guide.com/e/e2027.html

Transportation within Tokyo:
http://www.japan-guide.com/e/e2017.html

Buy the rail pass as advised BEFORE you travel.
You "covert" your voucher at Narita airport or other key sttions. You can reserve all your tickets there or do them later. (reservations easy - especially if you travel outside the rush-hour) If you search the internet you can even downlaod the rail timetable in advance. Travel on "Hakara" trains - very fast, comfortable and reliable - and VERY punctual.

Thanks for your advice.
Should I spend 1 night in Kyoto; then 1 night in Osaka. Then return to Tokyo directly from Osaka?

Pick up EITHER Kyoto OR Osaka as a base in Kansai Region, so that you dont need to bring your luggage from one hotel to another.