Traveling around in Japan?

Question:

I'm planning my trip to Japan but I really know little about their transportation. I've seen people mention JR pass but that's 45,000 yen! Too much for my low budget. So how can I travel around? Lets say....
Just around Tokyo for about 10?
From Nagano or Gunma to Tokyo?
From Nagano or Gunma to Tokyo and then back later the next week?
From Nagano or Gunma to Tokyo and later Kyoto?
Thanks for any help but I hope to get good answers as I'm clueless to this and can't find help!

Answer:

How do you get to Nagano or Gunma prefecture from Narita (Airport) in the first place?
If you want to go to one of the prefectures directly from Narita, you need to take slow local lines by changing trains from one to another all along the way. It sure is a very complicated and time-consuming travel especially for foreigners who have language difficulties in Japan. I would not recommend it.
You should come to Tokyo first. From Tokyo, you can go to both Gunma and Nagano prefectures fairly easily by taking bullet trains (shinkansen).

But I'm afraid if you really know how to get to your "ryokan onsen" that are located in remote areas from Shinkansen stations. In case of Joetsu Shinkansen, there ae only two stops in Gunma prefecture. You will get off at one of these stations, but you still need to take local transportation (either trains, bus, or taxi) to get to your destination. Even if you get lost, nobody would help you in English. Are you ready?

BTW, your plan #1: "Just around Tokyo for 10 days" seems to be the worst plan. As a Tokyo resident (born in Osaka), I can tell that 3 days is enough for a sightseeing in and around Tokyo. You should visit Kyoto, Osaka and Nara areas as well. If I were a foreign visitor to Japan for the first time, I would Travel Around Japan by making the most of JR Pass for two weeks. JR Pass is incredibly (or criminally) cheap when you realize the fact that1) Tokyo-Osaka round trip ticket is around 25,000 yen, and 2) Tokyo-Nagano round trip (by Shinkansen) is around 15,000 yen. What if you can continue this gorgeous trip from Hokkaido to Okinawa for two weeks @ flat rate of 45,000 yen? It's a crime! I wish I could buy the pass.