I'd like to give my guys big beards, but Franklin appears to be the only one capable of growing it out. Does my choice of barber affect my choice of hairstyles? Will more customization options be available later in the game, or are the choices within each store static and based on character? Is Michael ever able to rock anything more than the stubble?
The customisation options for the 3 main characters of the single player game does not change. All barbers will have the same options.
The reason for this is because while Rockstar wanted you to be able to customise the characters, their customisations still had to be fitting with the sort of hairstyles/beards/clothes that that character would wear.
There are some outfit options which you will unlock when doing specific missions, such as a police trooper outfit and trashman outfit.