Hansa in pretty much every city for me, it's usually the first thing I build once avail.
However, on a coastal city with lotsa sea resources, I my do a Harbor first (shipyards are crazy now)
Even I do harbor first, hansa is always next. Then I decide what else once the city grows.
Of course if you got the +2 production to factories, then yep them everywhere. (same for a +2 culture for factories, that one surprised me)
I'll take a CS I don't need/want (or to take away from the AI).
With all that production, dom is rather easy. (you can also then spam theater districts, and then send waves of archeologists and go for culture)
Science not too bad either.
Production up fast, means you can do whatever you feel like afterwards.
I try to get 3 slingers/archers fast, at least 1 scout (first thing I build)
Second city up once I'm pop 3, but timed so that pop 4 happens just before the settler drops.
After that, depends what the AI does. One game, all I did was spam archers since everyone was DoW me.
After wiping out everyone on my continent (DoW that early, yer gonna die), it was stupid.
Got extra campus and holy sites for free basically.