As for EU citizens, my feeling is that those in this country who already have a National Insurance number and are working legally will be allowed to continue living their lives unmolested, but EU citizens who want to move here and find work in Britain post-Brexit will have to jump through a few more regulatory hoops than they currently do.
I think you are probably correct - that is what I also would expect to happen. However even that leaves potential problems. Most obviously, many of those who are already here and would satisfy the requirements for being allowed to remain will have girlfriends, boyfriends, husbands, wives or other family currently back in their home countries. What will happen to those people? Anything short of keeping the current free movement rules in place (unacceptable to most Brexiteers) is likely to cause a lot of anguish and separation of families.
Also, any restrictions are likely to cause short term
increases in migration. Human nature being what it is, as soon as any hint of future imposition of the restrictions comes in, you can practically guarantee there'll be a surge of new migrants coming in to beat the deadline for keeping the right to remain living here. On a longer timescale, you'll probably see far more EU migrants applying for British citizenship - because with the UK outside the EU, they'll be more fearful of something going wrong and their losing their right to stay here if they don't.
You may also find that EU migrants become more reluctant to return to their home countries if their situation changes - again because they won't wish to jeopardize their future right to remain here. Currently, non-EU nationals who have permanent resident rights generally lose those rights if they remain abroad for 2 years. In the event of a Brexit and an end to free movement, the same would likely apply to EU nationals. I would expect that one result is that many EU migrants who currently come for a couple of years then return home would be more likely to seek to stay in the UK permanently, rather than return home and risk not being allowed back in the future.
Also bear in mind that if you want EU nationals to be subject to some kind of quota/points/skills system for resident rights in the UK, that would imply a significant increase in bureaucracy within the home office.
I'm sure many Brexiteers will see those are relatively minor issues, but they do illustrate that removing free movement is unlikely to be quite as simple as you might hope for.