US volunteers to test first vaccine according to this article BBC

Dr John Tregoning, an expert in infectious diseases at Imperial College London, UK, said: "This vaccine uses pre-existing technology.

"It's been made to a very high standard, using things that we know are safe to use in people and those taking part in the trial will be very closely monitored.

"Yes, this is very fast - but it is a race against the virus, not against each other as scientists, and it's being done for the benefit of humanity."

There is a non zero risk of death. There have been cases where some candidates had severe permanent damage and it took a while to figure out why. We are all slightly different.

Even with animal trials there is a risk. I do not think there is an answer to your question.

The risk very likely depends on exactly what the vaccine is.  A universal policy is likely not warranted.  Moderna was designed in 2 days.  Note what the vaccine is.  vaccine = (carrier RNA + selected viral genes).  The carrier RNA has already been tested and shown to be safe in humans.  The selected viral genes are going to be expressed in your body if you get the virus, without your consent anyways, so getting the vaccine by definition is safer than getting infected.  

We lost hundreds of thousands of lives because the FDA choose to apply a one size fits all policy - protecting their own reputation and the careers of a few people - instead of realizing this and making the correct decision.