Hi Michael,
For a trip like this you'll need to spend over ¥28,300 on individual JR tickets for a 7 day pass to be worthwhile. Lets take a look at your costs:
-
Narita airport terminal 1 > Tokyo: ¥3140, (62mins, 79km)
-
Tokyo > Nara: ¥13950, (225mins, 555km)
-
Nara > Kyoto: ¥690, (44mins, 41km)
-
Kyoto > Osaka: ¥540, (28mins, 42km)
-
Osaka > Kansai airport: ¥3340, (57mins, 64km)
JR ticket cost: ¥21660 for 5 legs
As you can see you'll need to spend a further ¥6640 on JR tickets for a 7 day pass to be worthwhile. If your itinerary is fixed, I would recommend individual tickets. If you think you'll do any further travel it may be worth using a 7 day pass - a return trip to Hiroshima for example would more than make a 7 day pass worthwhile for example.
If you do decide on single tickets, you can purchase these simply from the JR ticket office on arrival at a JR station in Japan. You can purchase in advance, or on the day of travel. Provided you are not intending to travel during rush hour times, I would recommend you purchase them on the day of travel.
Hope this helps!