The Cheapest way I think would be to take the Keisei Local (not the Skyliner) from Narita to Nippori. It will cost you 1000 yen.

http://www.keisei.co.jp/keisei/tetud...o_express.html

When you get off at Nippori, go on the Yamanote Line to Shinjuku, that will cost you 190 yen

Total return will be 1190 x 2 = 2380 yen. I think this is your most economical way.

If at the end of the day, you need to go back to NRT faster, you can catch the Skyliner (also from Nippori) for 1920 yen. But if you check the schedule, the Keisei Skyliner is only about 20-25 minutes faster than the 1000 yen local train. So it depends on your schedule. If you go on their website, they have all the times for both trains.