Hi Loic,
Yes, I think a 14 day pass will likely be the best option for you, bearing that it will be valid from the 29th Sept to the 12th Oct to get the most value out of it. Here is the cost breakdown for you. I have assumed you will be going to Kawaguchiko for Mt Fuji, but you could also go via Gotemba.
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Tokyo > Kamakura: ¥2100, (47mins, 51km)
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Kamakura > Odawara: ¥740, (49mins, 41km)
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Odawara > Otsuki: ¥5810, (109mins, 132km)
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Otsuki > Nagoya: ¥12520, (211mins, 414km)
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Nagoya > Kawarada: ¥740, (44mins, 44km)
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Kawarada > Nagoya: ¥740, (47mins, 44km)
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Nagoya > Kawarada: ¥740, (44mins, 44km)
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Kawarada > Nagoya: ¥740, (47mins, 44km)
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Nagoya > Kawarada: ¥740, (44mins, 44km)
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Kawarada > Nagoya: ¥740, (47mins, 44km)
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Nagoya > Kyoto: ¥5640, (37mins, 147km)
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Kyoto > Kanazawa: ¥6910, (124mins, 224km)
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Kanazawa > Nagano: ¥15310, (250mins, 473km)
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Nagano > Tokyo: ¥8170, (106mins, 222km)
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Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
JR ticket cost: ¥64780 for 15 legs
- 14 day rail pass (¥45,100) saving: ¥19680
Getting to and from Suzuka Circuit from Nagoya with JR Pass
To get to Suzuka circuit from Nagoya you should aim to get to JR Kawarada near the Suzuka circuit with your Japan Rail Pass (sample itinerary). From Kawarada station you'll need to use the local non-JR Ise Testudo operated line to get to Suzuka Circuit Ino (sometimes written 'SuzukaSakittoIno' (sample itinerary). As this is not covered by the rail pass you will have to pay the standard ticket fare of ¥300 each way. From Suzuka Circuit Ino you can easily walk to the circuit.
Getting to Hakone with a Japan Rail Pass
A Japan Rail Pass will take you as far as Odawara station for Hakone. From Odawara you'll need to use the non-JR Odakyu lines up to Hakone itself. I recommend the Hakone Free Pass for your travels as it covers all the funiculars, cablecars and trains and also has discounts on many attractions. You can purchase the Hakone Free Pass at Odawara station on arrival.
Getting to Kawaguchiko (Mt Fuji) with a Japan Rail Pass
A Japan Rail Pass will take you as far as Otsuki station for Kawaguchiko. From Otsuki you'll need to use the non-JR Fujikyu lines up to Kawaguchiko. Here is a sample itinerary for you.
Best travel option for the first few days
For travel on the first few days you should look at the [Narita Express + Suica metro card] deal which you can purchase from the JR ticket office on arrival at Narita Airport. This will cover your trip into Tokyo from the airport and give you ¥1500 of free metro travel which should allow you to explore Tokyo until you activate your rail pass.
More routes and fares
You can look up precise train timetables and costs at the Hyperdia travel planning website and learn how to use Hyperdia for JR Pass holders through our video blog.
Hope this helps!