Following up to this answer, given that a newly conquered city will
- spend a few turns of zero production (“rioting”)
- after that, will be hampered in production because of diminished population and destroyed buildings, so that building a courthouse will take very long
is there any point really to annex a newly conquered city immediately?
Doesn’t it make much more sense to first puppet the city and then wait – say 10 turns – until things have evened out and only then annex the city to start the courthouse?
EDIT: One aspect that I didn’t ask for explicitly is whether you should always leave the city as puppet until the rioting stops (typically 2-5 turns in my games so far)?
I’ve been thinking about it myself, and I agree that it’s almost always a better option to let the city stay as a puppet for a while before annexing it.
One major drawback here is not only that you cannot control what puppets produce, but it’s that puppets never produce units. If you’re at war, for example, the ability to produce units is critical, and sometimes you just need the extra city right now. Still, considering that conquered cities lose half their population and most of their buildings, their production is usually so low that making them a puppet is probably still the best choice.
Regarding the edit: I see no reason for annexing a city before the riots are done. You can’t do anything during riots anyway, so it’s best to not lose the extra happiness for these few turns.
However, now WillfulWizard’s answer becomes more important. If you intend to annex it soon but you want to keep it a puppet for just 2 to 5 turns, there’s a good chance you might forget – particularly if you’re in the middle of a war and every turn is hectic and eventful. If you intend to annex it quickly anyway, maybe it’s best to just lose the few points of happiness from having the city annexed during its riots, than to forget about it completely.