The reading for 選 is what you'd expect. 手 is the on'yomi reading as it is every once in a while, especially when it has to do with representing a person, so you'll have to remember that. I think you've seen 手 using this reading enough to be able to remember it, though.
Who is that handsome pro athlete?
These days, we can often see Japanese professional baseball players play in the major leagues.
Koichi is magnificent pro kendo player.