Do you mean you want to take the JR Narita Express to Shinjuku, then change to the Toei Shinjuku Line to Akebonobashi? If that's the case, you might buy the 'Suica and NEX' package for 3,500 yen.
Suica and NEX
Suica and PASMO info
This package includes a Narita Express ride to Shinjuku in your case, a suica card (500 yen refundable deposit) and 1,500 yen suica credit.
After exiting the JR side at Shinjuku, you can enter the wicket on the Toei Shinjuku side with the suica. When you exit at Akebonobashi, the fare will be automatically deducted from the credit.
I always recommend this package to other foreign questioners who will land at Narita and that ask for convenient and reasonable mode of transport to central Tokyo.
Why I didn't mention this package to you is because Akebonobashi is located on the Toei Shinjuku Line which is well connected to Keisei Line at Motoyawata, and it's reasonably priced as well. On top of that, at Shinjuku, as soon as you get off the Narita Express, you first go upstairs to the overhead hallway to the South Exit, and walk to the Shinjuku Line platform which is located deep underground, though you can utilize escalator all the way. The transfer takes at least 10 minutes and the station is always packed with people
JR Shinjuku Station map: Narita Express arrives at platform #5 or 6.
NEX timetable
Hope this helps.