Hi there!
Lets take a look at your costs:
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Narita airport terminal 1 > Shibuya: ¥3,110 (85mins, 93km)
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Shibuya > Kyoto: ¥13,220 (177mins, 514km)
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Kyoto > Nara: ¥690 (45mins, 41km)
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Nara > Kyoto: ¥690 (45mins, 41km)
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Kyoto > Kobe(hyogo): ¥3,240 (54mins, 75km)
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Kobe(hyogo) > Kyoto: ¥3,240 (54mins, 75km)
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Kyoto > Hiroshima: ¥10,590 (112mins, 380km)
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Hiroshima > Osaka: ¥10,220 (109mins, 345km)
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Osaka > Kansai airport: ¥3,340 (57mins, 64km)
JR ticket cost: ¥48,340 for 9 legs
As you can see you'll make a small saving with the 14 day pass if you do your full itinerary. If you need flexibility for the 14 days, then I think the 14 day pass is a good choice. If you were really on a budget and don't think you need as much flexibility for the full 14 days, you could use a 7 day pass between the 15th and 20th and make really good savings of around ¥13,590 on the travel you have planned for this time. If you go for this option I recommend looking into the [Narita Express + Suica deals] or the Keisei Skyliner + 2 day metro pass deals to get you into Tokyo and give you discount travel while you are in town.
If you do go with the pass, all seats will be covered, and for JR Pass holders seat reservations are 100% free during the validity period so you would not incur further fees.
I hope this helps!