Am I looking for a Transgender, a Transexual, or what?

My wife and I were discussing the possibility of adding a third party to the bed at night, for added flavor and to keep the sex life new, when we came across the mutual agreement(much to my surprise) that we would prefer to have a (apologies if this is a derogatory term as I am new to this idea) She-male as opposed to a specific gender. Now the kind of person we are looking for are the ones with feminine bodies, breasts, and a penis. however I have been unable to find a definitive answer as to what I am looking for and don't want to end up asking for the wrong thing. Which term should we use in the personals add. (Once again my sincere apologies for any ignorance which may be offensive in this post as we are new to this idea)