There is a ton of information on the web about vaccines and it is difficult to navigate and decide who/what to trust. Fortunately, rather than have to trust anything any particular person, news article, or website says, I can point you to some scientific information from multiple independent sources that can answer your questions about vaccines.
The first thing I tell my friends that are young parents is to go to the US Centers for Disease Control website, the CDC is a great source of information (links below). Also, if you want to dive deep into the specifics of vaccine safety, there was a large study done by The Institute of Medicine, which is in their words “an independent, nonprofit organization that works outside of government to provide unbiased and authoritative advice to decision makers and the public.” For the Institute of medicine study a group of scientists (including my advisor Pejman Rohani) investigated the immunization schedule and vaccine safety. It is a very long detailed report (200+ pages, PDF here). They also have a brief summary of their results here.
Below I have also included a link to the European Centers for Disease Control which addresses vaccine safety. Another great basic information site is the March of Dimes, which is a non-government organization dedicated to all aspects of infant health.
Lastly, just in case you want to see the impact vaccines are having by saving lives of children in countries where health care isn’t as readily available and childhood diseases are much more rampant, I have provided websites for UNICEF (United Nations Children’s Fund) and the Bill and Melinda Gates Foundation, both organizations that work around the world to combat childhood diseases.
US Centers for Disease Control Vaccine Information
The March of Dimes Information Page on Vaccines
European Centers for Disease Control Immunization Information
Vaccination Campaigns by the Gates Foundation
United Nations Children’s Fund Vaccination Campaigns
Below is a fantastic infographic made by the students of The Last Mile Code.7370.