From Gunma to Korankei

From Gunma ken what is the advisable way to go there in korankei and Hotel to stay with?

It depends on your preferences (e.g. budget vs. comfort).

I personally would take the shinkansen to Nagoya, stay at a nice hotel in Nagoya and access Korankei in a day trip by subway and bus via Toyota-shi:

For lower-budget travelers, there is a direct overnight bus between Gunma and Nagoya. But it could even be cheaper to take regular trains down to Tokyo and then a low-budget bus from there to Nagoya, because high competition on the Tokyo-Nagoya route produces even lower fares.

If you are a group of people and want to save money, driving there could be the cheapest.