I can appreciate your position, and I think this is literally the default- "I don't know much about vaccination, I'm told it's safe and effective, and I assume the same."
Regarding finding quality information, it exists but is sometimes hard to parse out. Surprisingly, a lot of "anti-vax" sites actually source their facts (e.g. specific research studies) so you can fact check on your own their claims (unlike a lot of pro-vax sites). Be careful, ANY site/person who questions vaccination in the slightest is labeled "antivaxxer." Here is a pretty decent, objective site:
http://vaccinepapers.org/
In my opinion, the real challenge lies in the fact that we have very limited understanding of what harms actually DO come from vaccinating, and the research into this phenomenon is "inadequate" per independent review.
https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD004407.pub3/abstract
We do know that vaccination does lead to a variety of harms (different dangers come with different vaccines), unfortunately our monitoring systems are severely flawed and estimated to catch as few as 1% of actual vaccine injuries. I have had some difficulty finding good research on this topic (vaccine injury underreporting) but remember research showing around 40% of vaccine induced polio was not recognized as such:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1615747/?page=2
That's a pretty big deal when you think of more subtle vaccine injuries (e.g. seizures).