Like Mike said, any one of those rings will work for the back of the bow if there are no violations.
Sure, that thicker ring looks attractive, but those are tiny staves, unless you've got enormous thumbs
So the more rings you remove, the more width you lose, and the less wood you will have to shape a handle with.
My first notion with osage is always to remove the bark and sapwood and seal the back. But in this case, since they are so small, I would remove the bark, and then do some measuring and planning first. If I felt I needed to, I may elect to leave the sapwood on them. If I could make the bow I wanted without the sapwood, I'd remove it.
How long ago was this osage cut?