Questions about travelling from Tokyo to Osaka and where to stay at?

Hello, me and 3 friends are planning to go to Japan for 14 days in June this year. We will be arriving to Tokyo and departing from Osaka. We also want to visit Kyoto for a few days. I have some questions to make a proper plan.

1. We are on a little bit of a budget and want to spend minimal money on transportation. I saw that plane tickets from Tokyo to Osaka are a lot cheaper than taking the Shinkansen. I took the Shinkansen last year and it felt very expensive, so I wanted to go for a cheaper alternative this year. Is it recommended to fly between the cities?
   Also, if we fly would it be better to use a luggage delivery service or just pay extra for more luggage on the plane?

2. We will probably do 7 days in Tokyo and 7 days in Kyoto/Osaka. I was planning on staying in either Kyoto or Osaka and doing a few day trips to the other place. Where would you recommend we stay at? Or would it be better to maybe separate it like 4-3 days and get 2 hotels?

Thank you in advance! Any recommendations are appreciated.