If I am interested to travel around Hokkaido, what is the best mode of transport? Self drive or via rail?

I am a fan of rail travel since I did my Europe rail travel, the shortcoming is just to visit rural area which rail and public transport would be limiting.

Roughly how much it cost to stay in a good Hostel?
Is 10 days good enough to do a not so rushed itinerary in the Island?

Thank you

Learned the hard way, don't try to over extend.. Just be happy of what you have planned.. If you want to cover more extend your days =)

Was so tired and started to get frustrated when I try to cover 11 cities in 25 days during my Europe tour.

Would 10 days there with a budget say 6~8k be sufficient? inclusive of air ticket too.
I would like to do a long distance run event (marathon or half) then continue on with my tour