Have not done that one, but did do Osaka to Kyoto last month to tour the temples. Some of the train lines offer a "tourist" train pass which is much cheaper. I think it was a 24 hour pass. DO NOT tell them you are there working (crew) because you are not allowed to purchase it. Bought it right at the airport.
You can buy 1st class and "coach". Watch the signs when you board.
Use the high speed trains. Our ride was 45 minutes vs 3 1/2 hours.