Hi there!
Lets get a handle on your costs:
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Narita airport terminal 1 > Tokyo: ¥3140, (62mins, 79km)
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Tokyo > Hakata: ¥21920, (366mins, 1174km)
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Hakata > Hiroshima: ¥8900, (69mins, 280km)
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Hiroshima > Kyoto: ¥10990, (126mins, 380km)
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Kyoto > Osaka: ¥540, (28mins, 42km)
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Osaka > Tokyo: ¥13950, (194mins, 556km)
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Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
JR ticket cost: ¥62580 for 7 legs
- 14 day rail pass (¥45,100) saving: ¥17480
- 21 day rail pass (¥57,700) saving: ¥4880
As you can see you'll make good savings with either option.
Route analysis
Of the two options, I think a 14 day + other option for your Tokyo travel is the best. Based on your savings, if you go with a 14 day pass you'll need to spend another ¥12,600 on transport within Tokyo to make a 21 day pass a better overall choice. You would easily hit this if you included a return trip to Nikko for example, but you may not manage to spend this much if you stay within Tokyo itself.
Recommendation
If you are happy with limited travel flexibility until the 8th, I recommend:
The N'EX+Suica vs Keisei+unilmited metro really depends on how you think you'll travel around Tokyo. The NEX+Suica gives you ¥1500 of metro travel, which is about equal to 8 rides on the metro and JR lines - it can also be used in convenience stores to purchase snacks/drinks. The unlimited Metro pass allows unlimited travel for 2 days, but is limited to the metro only and can not be used for other things.
Hope this helps!