It depends if transfer is a problem for you.

The reasonable one is to use Keisei Skyliner, they have a tourist package which includes a 1 Day Metro Pass + Single Way NRT --> Keisei Ueon, then you connected to Tokyo Metro to Shinjuku, on return you go back to Keisei Ueon and get on Keisei Skyliner again, the return trip cost you 1920 yen which means 4020 all-in (which cover your all-day Tokyo Metro as well) You can always use slower "fast" train for Keisei but considering your 1 day mad-dash I won't recommend

Package Information : http://www.keisei.co.jp/keisei/tetud....../index.html

For JR + Suica to ease your access, the package comes at 3500 yen but the Suica only contains 1500 yen, while the 500 yen deposit is refundable (face value refundable at 210 yen handling charge), it will be quite complicate procedure to get the maxinum value, plus you missed the all-you-can-travel Metro pass which comes in handy for 1-day Tokyo mad-dash

NRT --> Shinjuku : Package Discount Ticket
Assume no local transport / other use of Suica
Shinjuku --> NRT : Get the NEX ticket using the vendor machine, put in the Suica first to "burn-out" the value of Suica and top-up the remaining (1810 yen)
Go to the ticket office and ask for cancel and get back the 500 yen deposit (which ends up the total cost for the day is 4840 yen)