I've heard nothing but good things about Norwich. I just moved to East Thetford, which is about 10 miles north of Norwich. It's a very small town, largely rural but I like it. It is just beautiful here.
Norwich will probably be a bit pricier than the surrounding towns, as its location is so desirable, being right across the river from Hanover. Quechee and Woodstock are very nice towns, but also pricey.
If you have not already, check out the Dartmouth College housing website - it's the most comprehensive listing in the area.
It's at
www.dartmouthre.com, click on Upper Valley Rental List, Search for a Rental, and enter your criteria. It looks as if it's going to cost you around $1500-2000 to rent a house. If you can afford that, you'll be fine.
Also there is an organization called Housing Solutions Plus, which was very helpful to me,
www.housingsolutionsplus.com. I believe you have to contact them first to get a login name and password, but it didn't cost me anything to register.
I hope this info is helpful to you!