Hi, MHM,
Be careful with e-mail. I personally would prefer to receive a nicely written letter in the postal mail, with your e-mail address included so that I could be the one to initiate e-mail correspondence. Nevertheless, just be sure to prepare your e-mail messages as formally and carefully as you would a printed letter. Nothing irks professors more than to receive an e-mail message from someone who has not bothered to write it correctly and follow good writing protocols. I say this because a great many people have the tendency to write e-mail messages with extremes of informality, such as by neglecting to capitalize words, neglecting to re-edit the message before it goes out, neglecting to provide proper salutation, and neglecting to include all relevant detail so that the reader does not have to wonder what you mean.
By all means, also make sure that your proper name appears in the "From" field. Too often only the e-mail address itself is visible because the sender has never bothered to update his e-mail preferences to include what name to display when each message reaches its destination. E-mail yourself to see what it looks like.
Off the top of my head, I would say that the best letter includes at least the following elements:
1. Clues that you are motivated to do research.
2. A general idea of what major you are after, while acknowledging that you would be open to other possibilities in business as well, as you learn more about what the university has to offer. Do not try to be too specific. It's the school's job to guide you in the best direction after you arrive.
3. Openness to ideas of all types. Do not make it look as though you have already selected your specific line of research.
4. An idea of what you want to do upon graduation. The answer is supposed to be something like, "I wish to pursue a career dedicated to research."
5. No errors of any kind.
Do not ask any information that you could verify by visiting the campus website, such as how to apply or what the fees are. I suppose this means that you should first study the website and figure all of this out. You do not want to ask the professor anything administrative. It should all have to do with your interest in doing research. Of course, it is also an excuse to tip the professor off that you have a high GMAT score.