How to get from Narita Airport to Akihabara?

What is the best way to get from Narita Airport Terminal 1 (after 19:15) to Akihabara? Should we take JR East toTokyo Station and transfer to Akihabara via JR Yamanote Line? Can JR East tickets be purchased by credit card upon arrival at the airport terminal kiosk since the service center closes at 19:00?

You should ride either Keisei or JR and arrive Ueno station or Tokyo station. Akihabara is 2 stop from both Ueno and Tokyo.
http://www.japan-guide.com/e/e2027.html

Hi, the easiest way id to catch the Keisei Skyliner train from Narita. It gets to Ueno in under 40 minutes. Then from the Keisei station exit you could walk 15 minutes to Akihabara along Chou Dori, a busy and interesting shopping street, or catch the JR Yamanote line train from JR Ueno, it's just two stops. It would be much more fun to walk though.

When is your plane scheduled to arrive? Which place near Akihabara Station are you going to reach?

I do not recommend you make a transfer in Ueno.
Keisei Ueno Station and Ueno Station of JR-East are located a bit apart, and Ueno Station is complicated.
Nippori sounds better for a Keisei-JR transfer.

What is the best way to get from Narita Airport Terminal 1 (after 19:15) to Akihabara?

It depends on the definition of "best."

If you get a one-way Suica & N'EX package, you can reach Akihabara at 1500 yen.
However the way of the transfer in Tokyo Station is long, starting at Sobu Underground Track 1 or 2 on the 5th basement and ending at above-ground Track 3 or 4. Escalators are available on the way.
Akihabara is the second station after Tokyo.
All seats of N'EX trains require reservation.
- http://www.jreast.co.jp/e/suica-nex/index.html
- http://www.jreast.co.jp/e/stations/e1039.html

Access Express trains of Keisei are running to Keisei Ueno in the evening.
Using either a Suica Card or a PASMO card from Narita Airport, you can make a simple transfer through Transfer Gate in Nippori. Trains for Akihabara depart from Track 9 or 10.
Akihabara is the fourth station after Nippori.
The one-way fares are at 1350 yen in total.
Seats of Keisei Access Express trains are not for reservation.