Customizing your character might take some time, and the "racing" server is not the friendliest place for that. People just want to race there, and you won't have much time to change your ped.
Hop over to the "staff dev and rec" server, (see here) where it's usually empty.
That said, use the F6 menu to customize your ped. Do NOT die while you customize your ped, or it will be reset. When you feel that your ped looks good, save it in F7→Ped→Save. Your ped should also transfer to the racing server automatically.