For tournament play the max size is usually 3/4".
I remember getting a Marble King bag which said a shooter in every bag but it was hard to tell which marble was slightly larger than the rest. When I found it, I had the impression that it was close to 5/8" and the rest of the marbles may have been slightly smaller. So, for small fingers, shooters could be considered notably less than 3/4".
And then in the unofficial category, there is the common practice of referring to everything 3/4" and larger as shooters.
So how about that for covering every marble size higher than 9/16" ....