which pass should be pre-purchase?

Hi there!

If you are going to be staying and travelling within Tokyo for the duration of your trip I don't think a Japan Rail Pass is a good choice for you.

In order for a JR Pass to be worth it you need to spend at least ¥28,300 (7 day pass price) on JR train tickets. In general, this means at least 1 return journey on the bullet train will be required before it starts becoming an economical choice. As your destinations are all within the Tokyo metropolitan area, it is unlikely that you'll spend this amount on JR tickets.

Rather than the Limousine bus, you may also want to consider buying a [Narita Express + Suica metro travel card combined deal]. For roughly the same price as the bus, you travel into Shinjuku on the Narita Express train (a great modern rail experience), and also are given a prepaid travel card good for ¥1500 worth of travel on the Tokyo Metro or JR trains. This combined Narita Express return + metro card costs ¥5,500. As the normal total cost of these items is ¥8,220, you save ¥2720 if you choose this option. Another way to think about this is that you get your Metro travel for free! The Narita Express goes direct from Narita to Shinjuku station so it is a convenient choice.

You can purchase the Narita Express + Suica combined deal at the JR ticket office in Narita on arrival.

Hope this helps!