Which JR Pass to buy?

Hi, I will be in Japan for 21 days from 6-26 July and plan to cover mainly Hokkaido. I had wanted to take a flight direct to Sapporo from Narita but all domestic flights were full on the days I wanted. So, I have decided to enter Hokkaido via train instead.

My itinerary includes the following cities : Tokyo - Hakodate - Noboribetsu - Kushiro - Shiretoko - Wakkanai - Ashaikawa - Furano - Sapporo - Tokyo.

Upon arrival at Narita, I plan to take the train straight away to Hakodate. I will be staying in each town/city for about 2 to 3 days.

I am thinking of buying the 21 days JR Pass but I am also aware that there are other regional passes such as the JR Hokkaido Rail Pass, JR Hokkaido Free Pass, etc. Which pass should I get in order to enjoy more saving? Any advice will be much appreciated. Thanks!

The flights from Narita to Chitose may be full, but have you considered flying from Haneda (Tokyo's domestic airport) to Chitose instead. It is a much more frequented route that should have many flights available. Here's some info on flights from Haneda to Chitose:

http://www.japan-guide.com/e/e5306.html

And info on domestic air travel:
http://www.japan-guide.com/e/e2365.html