I found a way to manage citizen easily and effectively:
1) First of all you lock all tiles you really need to be worked. Those are usually Great Person tiles, luxuries, couple other resources, and 2-3 best farms.
2) After that you click automatic distribution of the rest of citizens.
3) Then you manually select specialists that you need to be worked.
And here is the trick: every time you click on Specialist - AI will take the worst citizen to become a specialist. That means that it is very easy to compare whether city benefits from this new specialist or not. Once you see that next specialist gives more bad then good - stop.
If doing so - you need to check every city only when it gets +1 population and you have notifications for that. This is very easy to manage!
As for the priority I'd say typically you always want to work all of your culture speciallists/ Other than that - it is really hard to give much advice.
I can say something like "you want your cities to be growing" or "production is more valuable than gold" but there is so many exclusions to that so it does not make much sense at all. For example you want you cities to grow at a speed of 1 cititzen every 7-10 turns on average, but it is okay to stop growing in Renaissance to focus on production. Lots of other similar stuff
