When will you come? On a weekday?
According to the current timetables for weekdays,
Keisei - Toei through trains leaving NRT in the morning after 8 am
mostly
skip Kuramae Station;
the 8:49 Access Express train makes a stop at Kuramae,
but after that there are no direct trains during the next three hours.
[Trains to get to Kuramae Station]
In NRT Terminal 1,
there are Narita Airport Stations of JR and of Keisei.
You can take two trains
from Narita Airport Station to Kuramae Station
on the Keisei lines + Toei Subway Asakusa Line.
You cannot reserve seats in these trains.
The seats are mostly long seats, each for up to 6 to 8 adults;
in some trains there are pairs of face-to-face seats, each for 1 or 2 adults.
Keisei Access Express trains for Haneda Airport
go by the (Keisei) Narita SKY ACCESS Line until (Keisei) Takasago
and continue beyond Oshiage onto the Toei Subway Asakusa Line.
Currently four Access Express trains are scheduled to depart
during the 3 hours from 9 am on weekdays,
and they all
skip Kuramae Station.
You can get off the Access Express train at Asakusa Station
and catch a train departing at the same track which makes a stop at Kuramae.
Alternatively
you can take a (Keisei) Limited Express train for (Keisei) Ueno
on the Keisei Main Line until (Keisei) Takasago Station,
where you can catch a train departing at the other track beside the same platform which makes a stop at Kuramae.
In Narita Airport Station of Keisei,
to take a train on the Narita SKY ACCESS Line,
you pass through just the entrance gate;
to take a train on the Keisei Main Line,
you pass through both the entrance gate and the intermediate gate.
Will the train normally be super crowded during morning 9+am from airport to Kuramae Keisei and Toei Subway westbound trains
may well be crowded around Oshiage Station during weekdays' morning rush.
I suppose you can avoid the peak of the crowdedness
by getting around Oshiage Station after 9:30.
[Kuramae Station and your destination]
Toei Subway Kuramae Station is divided into two parts,
for the Asakusa Line and for the Oedo Line.
The two parts are about 180 to 450 meters apart from each other,
practically like two stations.
- Map (in Japanese) of Kuramae Station
https://www.kotsu.metro.tokyo.jp/subway/stations/kuramae/i/solid.png- Vicinity of Kuramae Station on Google Maps
https://www.google.co.jp/maps/@35.704293,139.791367,17z?hl=en: The sign "Kuramae Sta." is on the Asakusa Line part;
you see the Oedo Line part above it.
I recommend you check carefully the location of your first destination.
A destination to the north of the Oedo Line part
may be too far for you to walk with luggage from the Asakusa Line part.
