Use the "/tellraw" command, like this:
/tellraw @a {text:"Choose your character: ",extra:[{text:"White",bold:true,clickEvent:{action:run_command,value:"/scoreboard players set @p Character 1}},{text:", "},{text:"Mustard",color:yellow,bold:true,clickEvent:{action:run_command,value:"/scoreboard players set @p Character 2}},{text:", "},{text:"Green",color:green,bold:true,clickEvent:{action:run_command,value:"/scoreboard players set @p Character 3}}....]}
and so on...
Basically, this would display the text: "Choose your character: White, Green, Plum, Scarlet, or Peacock
Clicking on a name would set a scoreboard objective for each player to a respective value, and another set of command blocks somewhere else could teleport them and do other things like give them items, or change their XP level.