As someone who has some experience with clinical trials and drug approvals, I'd be quite comfortable taking the vaccine. A clinical trial size of 40,000 (20,000 receiving the vaccine) is way larger than a lot of other drugs that people are comfortable taking.

Is there zero risk of serious side effects? Of course not, there never is. But the trial gives enough data to say the risk is worth the benefit.

Edit: The FDA has already hinted that their initial approval (EUA) may be restricted to certain populations where the risk-benefit is justified. In other words, they may not approve it for healthy, young adults where the risk of serious Covid complications is low. That "full" approval could come later after additional clinical experience is gained.