JR yamanote line fare

I am planing to visit Tokyo in early April. I think I will take Kensai train to Ueno and connect to JR Yamanote line to Shinjuku JR for Ibis Shinjuku. Wondering how much would the fare from Ueno to Shinjuku would be? Is this the best and economical way to go to the hotel from Narita terminal 1 ? Thanks?

I think I will take Kensai train to Ueno

It is spelled Keisei.

Wondering how much would the fare from Ueno to Shinjuku would be?

190 yen. You can look up train fares here:
http://www.hyperdia.com/

Is this the best and economical way to go to the hotel from Narita terminal 1 ?

If you take the Keisei limited train (as opposed to the Skyliner), it will be the most economical way, but I would not call it the best way.

A Suica&NEX package for a direct NEX ride costs just a few hundred yen more. The alternatives are explained here:
http://www.japan-guide.com/e/e2027.html?aFROM=2027_3011

Is this the best and economical way to go to the hotel from Narita terminal 1?

If you hope to have a reserved seat, a direct Narita Express train of JR-East is the easiest option. It takes about one and a half hour.
N'EX trains for Shinjuku are available from 07:44 to 21:44.
You can take one at 1500 yen if you use a ticket in a one-way Suica & N'EX package.
- http://www.jreast.co.jp/e/suica-nex/index.html

All N'EX seats require reservation. When Travel Service Center is closed, find a nearby ticket office with an icon like this.
- http://www.jreast.co.jp/net-de-teiki/receive/img/midori-kaeru.gif
Most westbound N'EX trains are two-destination trains.
Reserving your seat until Shinjuku, you will get on a car destined to either Shinjuku, Ikebukuro, Omiya or Takao.

Your N'EX train will arrive at Track 6. Your hotel is near West Ticket Gate, so please make sure to go downstairs (via an escalator) to the concourse.
- http://www.jreast.co.jp/e/stations/e866.html

I think I will take Keisei train to Ueno and connect to JR Yamanote line to Shinjuku JR for Ibis Shinjuku.

Keisei Ueno Station and Ueno Station of JR-East are located a bit apart.
A transfer in Nippori Station (though Transfer Gate) is far easier.

As to Keisei, you can choose a route among Keisei Main Line and Narita SKY ACCESS.

Taking a Keisei Main Line train (destined to Ueno) sounds simple, except that you will pass through both entrance and intermediate ticket gates in Narita Airport Station. The Keisei fare for a non-liner service until Nippori is 1000 yen.

The JR fare until Shinjuku is 190 yen. Yamanote loop Line trains for Shinjuku depart from Track 11.
- http://www.jreast.co.jp/e/stations/e1184.html

Thanks so much! I think I will take N'EX package. I will buy 7 day JR Pass for my 9 days trip. I plan to use it on Day 3 onward and will use it to go to Narita on the last day. I understand that JRP is valid for N'Ex from Shinjuku' right?

I understand that JRP is valid for N'Ex from Shinjuku' right?

Yes, it is valid on the NEX.

Thanks so much! I will take N'EX then. Actually, The trip will be 9 day trip. I plan to exchange JRP on the Day 3 for a trip to Kyoto, Nara, Osaka, Nikko, etc. I understand that the JRP is valid for N'EX from Shinjuku to Narita, right? Thanks!

I plan to exchange JRP on the Day 3

You will not have to wait until Day 3.
Unless it is too late at night, on Day 1 you can turn in your Exchange Order for your JRP by filling in a short application form and showing your passport with the Temporary Visitor stamp/sticker; you can also try reserving seats of N'EX and Shinkansen trains for the ways and the ways back. (Note that all N'EX seats require reservation.)
- http://www.japanrailpass.net/eng/en006.html
- http://www.japanrailpass.net/eng/en009.html

I understand that the JRP is valid for N'EX from Shinjuku to Narita, right?

Yes. But Narita is another station, which is located outside the airport.
The names of all the four stations in NRT (of two companies, in two terminals) each include "Airport."

Enjoy your trips!

Noted with thanks! It would be Natita airport station then. I will take Thai Airways flight leaving from Terminal 1 on Day10.