Hi there,
While the JR Kanto pass could help you save some money, it is only valid for three consecutive days, meaning you could not use it efficiently for your trip to Karuizawa as you plan to get there for 4 days.
The most expensive travel you will do is
Narita Airport --> Tokyo 3110 Yen
Tokyo - Karuizawa --> 5,750 Yen
Karuizawa - Tokyo --> 5,750 Yen
Tokyo --> Back to Narita Airport 3110 Yen
for a total of 17720yen
In this case it is probably best to get the buy the Suica & N'EX deal and buy your tickets locally for Raruizawa.
Or if you are below 25 years old JR east offers the JR East Pass for 16000yen for 4 flexible days of use.
http://www.jreast.co.jp/e/eastpass/
An other option is to go to Karuizawa by bus. This will save you some money for sure 2100-3000yen one way but can be hard to book if you don't speak Japanese.
www.japan-guide.com/e/e6030.html
Hope it helps a little.
-Daniel