For example, I've learned that certain noble positions will only be opened at certain population stages (mayor at 50 etc.), and that goblin sieges will not occur unless your population is equal to or more than 80. I'm looking for a list of these stages, but the wiki isn't giving me anything useful.
The first thing to note is that the game does not exactly have population stages as such. Certain events and nobles have requirements before they show up, and those requirements often include a certain population, but those are not exactly stages for the fort. There is such a thing as Fortress Rank, but that only changes some flavor text in the description of your fortress.
The nobles page of the wiki has population requirements for noble positions listed.
The fortress page of the wiki has a list of population to fortress type name equivalences.
In advanced world generation you can set population requirements for certain kinds of attacks. For example "Titan Attack Population Requirement." The default is 80.
As far as goblin sieges go; I have had sieges, "A vile force of darkness has arrived!", in fortresses where I had set the population cap below 80. It is possible that my population had exceeded 80 anyway due to dwarven births, etc., but the current siege page does not mention a population requirement, so I would be very careful about relying on sieges holding off till you exceed 80 dwarves. I have had Ambushes even before the first caravan, so care is always required.
In v0.28.181.40d the economy would start when you had 80 dwarves as well as some other requirements, but it has been disabled since then.
Here is a list of noble population requirements.
- Barron: 20
- Count: 20
- Duke: 20
- Mayor: 50
- Captain of the Guard: 50
- Monarch: 140
However you should note that some of these nobles have other requirements as well.
The information is rather scattered about the wiki, but the list on the nobles page has most of the information you are looking for.