Where are the statistics for vaccine side effects?
(World Health Organisation, 2014. p. 2) shows the adverse effect (side-effect) rates for the MMR vaccine. For instance, fever  between the 7th to 12th day after vaccination occurs in 5 to 15% of vaccine recipients and rashes occur in 2-5% of vaccines, etc. Page 6 summarises the results in a table. As you point out, the adverse effects are variable in severity and dependent on the particular vaccine; an organisation like the WHO will take into account the risk and severity of these adverse effects before recommending the use of the vaccine. And as you point out, it is not believed by the scientific community at large that vaccines have links with autism.
References
World Health Organisation. (2014). Information sheet observed rate of vaccine reactions measles, mumps and rubella vaccines.