The JR fees which you should pay are
the basic fare to get from Narita Airport / Airport Terminal 2 Station to Shimbashi Station
and the Limited Express surcharge to board a Narita Express train until Tokyo Station.
Alternatively you can take a Rapid train to Tokyo Station if available, which does not require a surcharge in addition to the basic fare.
A JR Rapid train leaving NRT which is to go beyond Tokyo Station becomes a Local train there and then makes a stop at Shimbashi Station.
For your leg until Tokyo, any seat of a Narita Express train can be reserved in advance, while any seat of a Rapid train cannot.
If you travel from and back to NRT within 14 calendar days mainly boarding a Narita Express train on each of the two ways,
you can save your JR cost by choosing a discount N'EX TOKYO Round Trip Ticket package.
This discount package includes two one-day one-way tickets, which can be valid for 14 consecutive calendar days and used to travel by JR lines within the usage area from and to any of the two JR stations in NRT.
Each of the two tickets works both as a basic-fare ticket and as a Limited Express ticket.
https://www.jreast.co.jp/e/pass/nex_round.htmlcan I use the same ticket? Yes.
Unless you go through an exit gate of a station on the way, you can travel all the way to Shimbashi Station either with one JR basic-fare ticket, with the first ticket in the discount package or at one session of using a Suica Card.
A regular Narita Express leaving NRT is to go beyond Tokyo Station.
Usually you can get off your N'EX train and can catch a Local train (which is to run in the direction of Shimbashi) via the same Sobu Underground platform of Tokyo Station.
Where is the best place to get the Suica / PASMO card? A Suica Card, JR tickets and the above-mentioned discount package are available in NRT, at JR East Travel Service Center in any of the two JR stations or, when the Center is closed, at the nearby JR Ticket Office.
You can also try to reserve seats of Narita Express trains there.
https://www.jreast.co.jp/e/customer_support/service_center.htmlCurrently there is no railroad station in NRT Terminal 3.
You can go between NRT Terminals 2 and 3 either on foot or by free shuttle bus.