The average bin man or Lidl worker is in contact with far more households, and more elderly etc, than the average school kid. As I say, it's easy to say put group X up the priority list, but you have to be aware that it has to be matched by an equal commitment to putting another group down the list.
You expect some reactions as the immune system sets to work recognising what's in any vaccine, and you tend to get more reactions in younger people as they have stronger immune systems. That's why one ends up with some vaccines having a lower dose for kids and a higher dose for the elderly, to tailor the response to the strength of their immune systems.
Fortunately the SARS2 vaccines seem pretty good as far as side-effects go.
You're right on one level, that hospital capacity is one of the things that should be used as a key metric - but at the same time you're ignoring the fact that 5-10% of all cases end up with long COVID, which can be hugely debilitating and potentially could be a huge drain on health resources in the future - like polio only worse.