How you look is part of what acting is, but the way I look at it, every actor is a character actor. Someone once told me at a casting, 'You're a character actor in a leading man's body,' and I can live with that.
My English teacher always gave me scripts for plays, but I was into sports. My friend said there were small parts I could go up for, but the director gave me the part of Mozart, which was kind of the lead role. From then on I just loved it.