There's been talk of prioritising certain groups for the vaccine when it starts to be issued, since the quantities required for everyone won't be there initially. I assume they mean front line hospital staff or the elderly.
The same has been said in Canada with respect to priorities of who gets the vaccine. There has been no official policy set however, and I suspect there won't be one until they know what vaccines will be available and in what quantities.
So from that I'd guess that over the long term not everyone would need it; just those most at risk, a bit like the flu vaccine.
The greatest benefit would come from everyone getting the vaccine in order to try to reduce the prevalence of the virus to as low a level as practical, and to wipe it out if possible.
There will be several problems. One is that vaccines often are not 100% effective. That is, some percentage of the people who get vaccinated will for some reason not produce the correct immune response and so will not actually be immunised.
Another problem, related to the one above, is that some people have weak immune systems, so the vaccination will do relatively little to protect them. These may be the elderly, those living with cancer or other diseases, and others. The vaccination "primes" their immune system, but it may still be too weak to fight off the virus.
However, if enough people get vaccinated effectively, then the rest are protected through "herd immunity". Yes this is like the herd immunity you would have if most people had the disease and survived it, but it's produced through artificial means rather than through having most people get sick.
The issue is going to be if enough people listen to anti-vaxxers and refuse to get vaccinated, we won't hit the 70% level (or whatever it is) required for herd immunity, and we'll still get outbreaks, although not as serious as we have now. It should be remembered by the way that a certain percentage of the people who do get vaccinated won't be immune because the vaccine didn't work effectively on them for some reason, so there isn't headroom for 30% of people to be anti-vaxxers.