There's a "JR Airport Narita" train from Shinagawa station to Narita airport.
Departs Shinagawa: 6.01am
Arrives Narita Airport: 7.37am

The above train is not a Narita Express. Expect a "commuter" train (bench seats).

Option 2 = Take JR Yamanote line to Tokyo station (connect to Narita Express)

Option 3 = Take JR Yamanote line to Nippori station (connect to Skyliner).

The Narita Express and Skyliner options are a few minutes quicker (leave later & arrive earlier) but cost more and requrie a change of trains.

If you want an extra 30 minutes in bed, I suggest a hotel near Tokyo or Nippori.
If you want an extra 90 minutes in bed, I suggest a hotel in Narita city.

Warning - Check all these times for yourself before making plans. Timetables are subject to change. Special trains run on some days. etc.