Hi.
It depends on your game, but basically if you load the player within a game scene.
then on main menu when player select you can save the selection as a int (start with 0).
(save in playerprefs for example)
then in game scene load (get) the value then use an array with the characters in it.
and use array get.
the saved int you need to set as the index.
so if 1st character was selected then it should be int 0, because an array start at 0 not 1.
Then create your player with the prefab you got from the array.