Early- Focus on aquiring pops in the first place, few regions are highly populated before warm period. Expand and build up your economy with surplus buildings
Mid-Focus on building more cities and developing them with foundries, grand temples & theatres, the specific ratio building you want etc... Then start slave raiding and sacking cities to gain the human and monetary capital to build up these cities. At this point you can start building up your state/provincial capitals with aqueducts
Late- Once world population has massively increased from warm period and AI development, you will have the resources and reason to develop your more peripheral cities.
In general they serve no purpose until you have the buildings and civ value to improve pop output more than the buildings that could be there or pops that could be elsewhere. The oppertunity cost is as always of lost output so make sure your cities are developed first before spamming aqueducts and avoid doing so on poor terrain provinces where thier effect is lessened. The smaller you are the earlier you will have fully urbanised and developed by virtue of having less territory to deal with so build up your aqueducts early to get the migration attraction for enslaved foreign pops which you should raid for regularly. Of course make sure in that scenario that you have the temple and theatre. For slave cities (cities built to generate trade goods) however you only need the foundry and mills so you can build aqueducts instantly on them but make sure to turn off slave promotion.
P.S Points 1 & 2 and 3 & 4 are pretty much synonomous so in future try to avoid this because it could be potentially confusing.