I did the headshot thing for a while in New York. Every city has its own conventions, so what works in other parts of the country may not fly here, and things have changed since I was doing it, now that there's more digital involved, so you'll need to do some research to see what's current locally. If you want to do business, you need to offer something that's competitive in the local market. A CD with hi-res images of all shots from the session is too much, I'd say, but a contact sheet is reasonable. There should be no issue of exposure problems with headshots, because you should be shooting in a controlled studio environment, where the exposure is always going to be about the same.
Look at the headshot ads in Backstage and talk to working actors, and see what kinds of deals the pros are offering. Usually it's a contact sheet and a master print (or more than one master print or a digital file with the selected prints), which the performer goes and has reproduced at a lab that specializes in headshot repros. Most photographers will offer to handle the reprints, but this is not really the interesting part of the business, so unlike wedding photographers, they get paid for the master prints, and the reprints are out of their hands. Also unlike wedding photography, the headshot business is about repeat business, because actors always need fresh headshots and may want special character shots for a particular audition.
Another thing to look at in the Backstage ads, and the walls of Modernage and Kenneth Taranto labs, is what the current fashions are in headshots. Do some shots with your own ideas, but most actors want the same damn thing that everyone else is getting, so learn to do whatever that thing is at the moment, and offer shots in that style. Kenneth Taranto (the best headshot repro lab) used to do an annual show of headshot photography. See if they are still doing it, and take a look at what's out there, and once you feel confident about your work, you might exhibit in the show.
New York is generally more conservative regarding headshots than Hollywood. On the West Coast, color, horizontals, and outdoor shots with natural lighting have been acceptible for quite a while. For a long time these were regarded as unprofessional in New York. Color has become more accepted in the New York market as photographers have gone digital in the last few years, and then I think you started to see more variety and natural lighting as amateurs without studios started getting in on the act.