Beppu-Kyoto-Tokyo-Beppu Transportation

Im currently living in Beppu, Oita and will have an itinerary as below
Feb 8th to Feb 12th: Kyoto
Feb 13th to Feb 16th: Tokyo
Feb 17th: back to Beppu

I would appreciate it if somebody could give me some advice/recommendation on the transportation for this itinerary. Specifically I want to make it as economical as possible and also want to try the shinkansen on this trip.

Thanks in advance :)

The shinkansen won't be most economical, for sure.

I recommend the following:

Beppu - (air from Oita Airport) - Osaka - (train) - Kyoto - (shinkansen) - Tokyo - (air to Oita Airport) - Beppu

It would be cheaper to replace the shinkansen ride with an overnight bus journey (you would also save on one night's accommodation):
http://www.japan-guide.com/e/e2363.html

As you probably know, Jetstar Japan has very low fares on the Oita-Osaka and Tokyo-Oita routes.

To even save more money you can take the shinkansen from Shin-Osaka station to Kyoto station.

If you want to experience a longer travel, you can get off the train at a later stop and without leaving the gantries, take the shinkansen backwards to Kyoto. May be illegal though, someone may have to clarify this.