Definately the range you wrote of. As someone else pointed out, this is a business arrangement for him, not a favor. He likely won't be answering the door in his scruffy pj's, hair scraggly, teeth not brushed, etc like he might spend another hour or so in the morning were it just him and his child working their way thru a lazy morning of Mickey Mouse pancakes, Sesame Street on the TV and a few minutes for him to read the sports page and drink a hot cup of coffee with relative ease in the comfort of his own home.
And the transporting/errands thing. Alot different when you are tied to another child, napping schedules (if any) and the prospect of your pick up time altering occasionally, etc.
I just point these things out further as I am a home childcare provider, and as much as I love my work and the families I serve, it is a job and ties you to your home in a different way. I have light fridays..only a few kids compared to my full week of them. But it is still a work day. Maybe your arrangement would be more casual, but I urge you to make sure things are all spelled out, so there are no miscommunications, etc.
Most providers I know will NOT do childcare for relatives, neighbors or friends. I learned that the hard way and never will again. It creates a different dynamic oftentimes. Yours is a one day a week situation, so perhaps that won't be the case. Just consider all the worst case scenarios and the what if situations and discuss them, I guess. I think if you do that, it will be fine.
I would pay him well and be that great "client" and friend all in one.
Good luck!