Have you ever heard of Sobu-Yokosuka Line? :) It is the least advertised, but the most useful in many cases. It is one of the cheapest methods, without sacrificing comfort. It is operated by JR East company, a member of the largest train company group 'JR', which also operates the Narita Express. Sobu-Yokosuka Line connects Narita Airport with Tokyo, Shimbashi, Shinagawa, Kawasaki, Yokohama, Kamakura and Yokosuka. This smooth connectivity can hardly be beaten. Unlike Narita Express, this train is also used for commuting, so morning trains toward central Tokyo and evening trains from central Tokyo to suburbs can be very crowded. But it is not a problem when you ride from Narita Airport, because it is the terminal station, and you can almost always find a free seat very easily, without reservation.

Again, the most important thing is that it is best connected - directly goes and stops at Chiba, Tokyo, Shimbashi, Shinagawa, Kawasaki, Yokohama, Kamakura and Yokosuka stations, skipping a lot of minor stations, just like limited express trains do. It runs almost every hour. So why not?

Firstly, because it is not advertised to tourists.
Secondly, if you take this train in the opposite direction - from central tokyo to Narita Airport in the morning or evening, a serious rush hours are waiting for you.

So, I do not recommend taking this train toward Narita Airport if you cannot keep your seat avoiding rush hours.
Note that Saturdays and Sundays don't have rush hours.

Buying a ticket for this train from a ticket machine at Narita Airport is kind of difficult. If you REALLY need a paper ticket, you can probably buy it at a counter near the gate.
I would recommend buying a 'PASMO' from a ticket machine of the Keisei Line, which is just 30 seconds away from the JR ticket machine. But does it work for JR? Of course! PASMO is completely identical to IC card SUICA by JR, and you can ride any trains, metros and buses in Metropolitan Tokyo including Kawasaki, Yokohama, Kamakura, etc. If you still prefer SUICA for any reason, perhaps you can buy it at a JR counter, but not from the machine, so ask staff.

When buying a 'PASMO', probably it's a good idea to charge at least 2,000 yen if you are going to Tokyo, or 3,000 yen if you are going to Yokohama, Kamakura or Yokosuka. This amount is a bit more than the ticket prices. But don't worry, you can get a full refund for PASMO at any time, including every penny of your deposit and balance.
And if you are from a rather cashless society, perhaps you can easily believe that you pay with PASMO at all kiosks and almost all restaurants, cafes and shops in and around train stations, as well as major convenience stores all over Japan - Seven Eleven, Lawson and Family Mart. No PIN is required on payment. It is more than a ticket. And you will never need to worry about the exact price of your ticket - it is automatically calculated and deducted.

You can go through JR gates and automatically pay with your IC Card 'PASMO'. It is functionally identical to 'SUICA' which is issued by JR, and you can use them interchangeably. When you arrive at your destination, touch your PASMO at the exit gate. That's all.

You can find a guide with photos on how to buy a PASMO from a ticket machine at Narita Airport at:
  Keisei 'Limited Express' Howto

For more about PASMO and SUICA see:
  How to buy and use PASMO & SUICA