There are no direct flights to either Kansai (Osaka) or Chubu Centrair (Nagoya) from the States; you have to land at Narita or Haneda.
I don't know if you are going to travel any further by train or is Kyoto a final destination with no prospects of further travel in the country.
If you do travel further, the
JAPAN RAIL PASS / ジャパンレールパス can be of value, since a round trip to Osaka from Tokyo on the Shinkansen is about the price of the pass for 7 days. You'll have to travel back to Tokyo to leave, so that's why I'm using that example.
The pass allows you to use any JR trains, with reserved or non-reserved seating, for the exception of the Nozomi service on the Tokaido-Sanyo Shinkansen. That means that any JR trains in Tokyo proper, Osaka and Kyoto will be free: just show the pass and you're in.
You can use
Hyperdia | 乗換案内 路線検索 時刻表 ゴルフ場 旅費精算 通勤費なら to find out exactly how to get there and how much it'll cost if you are not using the JR Pass.... For example, if you wish to depart Narita Terminal 2 at 2pm, you can take the Limited Narita Express #28 to Tokyo Station at 14:18 and arrive at 15:14, then taking the Nozomi 47 at 15:30 and arriving at Kyoto at 17:51.... The grand total would be 16,630 yen (about $204)....each way (per person)
As far as luggage is concerned, there seem to be places on the train cars that can accomodate them, but I'm not totally sure.
As to which is more viable, flying to Kansai or using the train, it all depends on the price of the flight package. The train pass is 28,300 yen (the exchange rate varies-$347 as of today)....