Just a question, where are you staying in Tokyo?
I just asked because, I want to suggest using the Limousine Bus instead. From the arrival area in Narita going to the platform is a few minutes walk and then there are the stairs too, with heavy luggage with you it is not fun.
The bus is basically just outside the arrival area and getting the ticket is much easier too. Someone will also stow your luggage in the bus for you.
there is also another train from narita, called the keisei line, have not used it personally but I heard good things about it and much cheaper than NEX.
anyways, lots of train and buses from narita to Tokyo, you won't have any problem
