The main question deals with sickness in the healthcare profession. With the exception of pediatrics, with universal precaution (and when needed, contact isolation gowns, and/or mask) you shouldn't have to worry about catching anything your patients have. Make sure you wash your hand frequently, and try to be self-aware of what your hand is doing at all times (try avoiding touching your own face/eyes/nose/mouth). You'll be surprised how often you do this without being aware of it.
For pediatrics, especially during cold-flu season, especially in outpatient pediatrics - you will get sick initially. You can wash your hand like crazy but the entire office (from door knob to table/chair/sink) is coated with snot from hands of sick kiddos. But just like teachers, daycare workers, parents ... with repeat exposures you develop immunity to the common bugs with time.
As for immunization - it is a good idea to follow the current CDC immunization guidelines. Hepatitis B vaccination (and in some cases, proof of immunity by quantitative HbsAb antibody) is require by almost all medical schools now and basically by all hospitals. Hepatitis B is 100x more contagious than HIV when it comes to needle sticks.
Once you enter clinical settings (basically from your 3rd year of medical school until you retire from practice), expect to get annual PPDs.
It would indeed be smart to be immunized against measles, mumps, rubella, and varicella. If you run into a kid with the active disease and you are not immunized against that virus, you not only harm yourself but also put additional patients at risk (this is especially true if you are taking care of babies or the elderly, or the immunosuppressed)
Tetanus shot should be updated every 5-10 years (the timing of a tetatus boaster is beyond the scope of this post). If you haven't received the acellular pertusis boaster within the last couple years (new recommendation), it might be a good idea to get it since there are some areas of the country where pertusis is making a comeback.
And get the flu shot every year. Not only does the flu make you VERY miserable, but the flu kills thousands of people every year. In clinical settings, your patients are vulnerable, in a weaken state and most likely fall into the category of high mortality/morbidity from the flu. You can give them your bug just as easily as they can give you theirs.
