I am a self employed contractor. I run my business as a sole proprietor with no home office or any other office. Would my business mileage start? At home or at the job?

If you had a home office, it would start from there. Since you don't it starts at the first job.

what if i have to stop for material or gas? Would this be where my business miles start?

If you must get materials, etc., stop at the first job and then do your business.