Doomsday,
Because you mentioned the “vaccine court” you ought to know that they keep public statistics of the claims they receive of alleged injuries due to vaccines and those claims that pay out on. Even if we assume that every claim is legitimate (almost certainly not the case as any litigator would tell you), the risk from vaccines is exceedingly small. For example:
1) between 2006 and 2016 there were 94,815,650 doses of the MMR vaccine given out in the USA. There were only 233 claims (valid or invalid) for injuries based on that vaccine. Even assuming that every claim is real, the chances of having an injury from the MMR vaccine is 1 in 406,934. You are far more likely to be struck by lighting (1 in 12,000) or even have siamese twins (1 in 189,000) than to be injured by the MMR vaccine.
2) The DTaP vaccine is a little more risky, with claimed injuries coming in at 1 in 376,112 doses. But Tdap is safer with claims of only 1 in 603,252 doses.
3) The Meningitis vaccine is much safer, with claimed injuries coming in at 1 in 1,655,250 doses. You are far more likely to win the Powerball (if you play weekly) in your lifetime than your child to have claim from the Meningitis vaccine.
All of these statistics are available on the Health Resources and Services Administration website. The upshot is that even under a conservative estimate, these are tiny numbers. Vaccines are extremely safe and far safer that not vaccinating at all.