Currently, this topic is highly controversial. That said, there is a plethora of information online regarding your concerns and questions. It would be best to talk with a pediatrician regarding vaccines.
The measles situation that occurred in Disneyland recently, has sparked an even more intense debate regarding vaccines and in response to that, certain states are re-evaluating the vaccine exemption laws.
The vaccine exemption is state specific and pertains to whether or not a family would be exempt from the mandatory list of vaccines required by the state (and recommended by the Center for Disease Control “CDC”) for your child to enter public school.
The decision process is one that will probably weigh the types of illnesses, the vaccines, the state requirements for exemption (if you fall into the exemption), as well as the injuries that rarely (but do) occur as a result of the administration of vaccines.
That information is very clearly set forth on the Health and Human Services website, which said entity oversees the Vaccine Injury Compensation Program (Vaccine Court). The vaccine court does pay people who are injured from vaccines, therefore, the potential injury is real (although a rare occurrence).
Your exploration may be complicated, but there are a lot of resources to utilize. One or more pediatricians, the Health and Human Services website, the CDC vaccination schedule, your state requirements and laws regarding vaccines and exemptions, and the United States Court of Federal Claims website that publishes its opinions for vaccine injury cases.