What style or system of Martial Arts is best for
The best system to choose depends upon the goals that you wish to achieve, however, my personal preference is a style that adapts to your body, not one that requires your body to adapt to it. Kenpo, Jeet Kune Do, Jujutsu, and Judo are examples of systems that adapt to your body.
What should I know about the instructor's credentials and belt rank,
and can he/she trace his/her lineage back to traditional systems?
For example, I am a 6th Degree Black Belt, with over 22 years experience in Kenpo alone. I was trained by John Conway, who studied directly under Ed Parker, who studied under William Chow. My point is that I can chart my training history, and ANY martial arts instructor should be able to show the same sort of proof of training. Keep in mind that a certificate only proves that that person has been taught by someone, and not that they are any good at martial arts or teaching. Also, do not be fooled by an "instructors" degree, or rank, of black belt. Any Black Belt can get promoted to a higher degree, if he/she knows the right person. Judge your prospective instructor by his/her attitude towards realistic training and display of professionalism, and NOT by the number of stripes on his/her belt.