As a data point of one, I had the Janssen/Johnson & Johnson single shot vaccine on March 5th with zero side effects. I didn't even get my typical sore arm at injection site afterward.
My partner had the 2-shot Pfizer sequence, with very minimal side effects. We know a lot of people who've received that one, and only two out of all of them did have side effects. Both were after the second, and both had flu-like symptoms. Both also said even afterward that they'll take that over Covid-19.
I only know one person in my circle, so far, that's had the Moderna 2-shot vaccine; no side effects.
Not that there's any perfect correspondence, but if you're someone who's had reactions to any vaccine in the past I would mentally prepare myself to potentially have the same to a Covid-19 vaccine. If you haven't, then the probabilities are that you most likely won't, but may.
In any case, it's better than getting Covid-19. My brother who's almost a decade younger than I am contracted it last June, and he's one of the long termers still dealing with after effects. His advice to me, even before the vaccines began rolling out: Do whatever you have to do to avoid getting this! Now that the vaccines are out, getting one is (or was, in my case) at the very top of the list of things to do to avoid contracting Covid-19 (or at least contracting it in a way that was likely to cause either hospitalization or death).