The schedule you list is reliable (mainly using the metro and the Keisei railroad), but does have some pretty nail biting transfers. Following route 1 you'll need to stay on the same train at Oshiage (The Toei and Keisei line operate a shared service, or "Through Train" that merges from the Toei subway onto the Keisei Oshiage line), and then transfer train at Keisei Takasago. You'll only have 1 minute for the transfer to platform 3 or 4 for the train to Narita, so will have to be on alert! You can find a guide to all the meaning of the icons on Hyperdia here.
As these itineraries are focussed at getting you to the Keisei line for the final stretch to Narita, you could also look at this route via Ueno, the start of the Keisei line. There's a short 5 mins walk(map) from Ueno subway to the Keisei Ueno station, but I think the transfers are more reasonable.
Hope this helps!