7 day pass or 14 day pass

Hello everyone,

We (3 of us) will be going to Japan for 14 days and 13 nights from 23rd Sep to 6th Oct this year.
Wondering whether we should buy the 7 day or 14 day JR pass.

Itinerary as follows:
Day 1: Arrive in Narita Airport--> Shinjuku
Day 2: Shinkuku to Hakone -> Planning to get the 3 day Fuji hakone pass here which also covers Shinjuku to Odawara.
Day 3: Kawaguchiko
Day 4: Kawaguchiko
Day 5: Kawaguchiko to Kyoto -> Take the bus express bus to Mishima and them take the shinkansen to Kyoto. If going for 7 day pass, this is where we were thinking of activating it.
Day 6: Kyoto
Day 7: Kyoto
Day 8: Kyoto to Koyasan -> Will be getting the Koyasan-World Heritage Ticket. Using the JR pass to get to Shin-Osaka only.
Day 9: Koyasan to Osaka
Day 10: Osaka to Nara day trip
Day 11: Hiroshima Day trip
Day 12: Osaka --> Tokyo (Ueno Park)
Day 13: Tokyo
Day 14: Ueno --> Narita Airport

Is it expensive to get to the airport and back without the JR pass?
Also, we will be having one large and one medium sized trolley bag. Any challenges in getting them along in the shinkansen?

Thanks