JR Pass - to buy or not to buy?

Hello and happy New Year!

I was hoping to get advice on the JR pass for my upcoming honeymoon trip with my fiancee. Please see our itinerary below:

Sat 18th March - Day 1 - Arrive to Tokyo Haneda Airport
Sun 19th March - Day 2- Explore Tokyo
Mon 20h March - Day 3 -Explore Tokyo
Tues 21th March - Day 4 - Explore Tokyo
Wed 22nd March - Day 5 - Explore Tokyo
Thurs 23rd March - Day 6 - Nikko bus day trip (with a tour guide)
Fri 24th March - Day 7 - Explore Tokyo
Sat 25th March - Day 8 - Explore Tokyo
Sun 26th March - Day 9 - Kyoto
Mon 27th March - Day 10 - Kyoto
Tues 28th March - Day 11 - Kyoto
Wed 29th March - Day 12 - Kyoto- Kōya-san
Thurs 30th March - Day 13 - Kōya-san
Fri 31st March - Day 14 - Kōya-san
Sat 1st April- Day 15 - Kōya-san - Nara
Sun 2nd April - Day 16- Nara - Osaka
Mon 3rd April - Day 17 - Osaka
Tues 4th April - Day 18 - Osaka
Wed 5th April - Day 19 - Osaka Kansai Airport

Should we get a 7 day or 14 day rail pass (or no rail pass at all and just purchase tickets as we go)?
And would it be wise to book any of these seats in advance?

Thank you very much for your advice!
V