Who gets the vaccine first is also about who the vaccine works best in. We know that different age groups produce varying responses to other vaccines & if this is true of a vaccine it may be best suited for younger generations rather than older generations. Hopefully we’ll end up with a few different vaccines that can cover the whole range, like we now have with flu, but again this could take time.
As for the imminent roll-out, well, approval of vaccines takes time usually after trials are completed, BUT, it’s possible to allow a roll-out to a limited group of people who are at the greatest risk of catching COVID-19 before final approval, and that would be doctors, nurses, etc.
Another thing to remember is that many current vaccines for other diseases carry risks, often pretty low, of adverse reactions. Flu vaccines have side effects, I find they vary from year to year, so, sore arm 3 days last year, swollen arm with pain & exhaustion for 2 weeks the year before. I can no longer have the tetanus jab either, I’ve developed a dangerous reaction to it over the years but I did have to have a vaccination every 5 years for my job, and the NHS used to give me extra jabs when they were stitching whatever bit of skin I’d ruined.