How to attach a "lean to" shed to a garage?
I see no reason to use Option 1.  My daughter would just find a way to loose her hula hoop (and everything else she owns) in that little space between the garage and shed. 

I like Option 2. Attaching the wall AND roof directly to something solid will keep the shed rigid. Also, having the back wall installed will allow you to fasten machinery and equipment to the wall without affecting the existing garage wall. 

Option 3 would give you a few more inches of floor space, but you’d have to “hang” everything directly on the garage wall. Also, if you ever decide to insulate the shed, you’d have trouble insulating the common wall.