There are the choices for backpackers and budget travelers.

TOHO house

TOHO house (in English)
TOHO house: map locater (in Japanese)



TOHO house is a network of the guesthouses ,50+ are all around in Hokkaido(See the below map). Aprrox. Yen 4000-6000 per night for 1 bed  incld dinner and breakfast(or optional).
Staying there is very close to a common style of people living in Hokkaido. Please note that you shouldn’t expect English, especially speaking, But you don’t have to worry, they are kind as same as people in the other countries you have been, eager to understand you.
They might be in distance from station or bus stop, it would be better to ask them pick you up when you book.

Hostels

Most of hostels are in the center of Sapporo. Approx.Yen 3,000 per night for 1 bed no meal incld. the below sites are in multi-lingual.

hostelz.com: Hokkaido Hostels  (E,F,S,I,D,P)
Hostels.com:Sapporo  (E,F,S,I,D,K)