What I did, though I was older than 7, was to start on a "baritone uke," but I cheated and tuned it to the top four (top in pitch) strings of a guitar-- DGBE. That way once I was sure I wanted to move on, my callouses were forming, etc., I already knew the top 2/3 of the chords. The only drawback to the straight uke or mando ideas would be if and when they switched, they would have to learn chords over, but then, there are multi-instrument performers in this world so maybe that's not all bad.

CC