I work a little differently than most for peaceful culture. I aim to have 10 cities of size 4 to 8 or so by the end of the game. Each city is responsible for 2 districts.
2 or 3 early cities will build campuses first (assuming you have decent adjacency bonus opportunities) then theater. 2 is nice in any case for the recorded history and printing boosts and a 3rd can get science up fast enough to get to needed techs early. 2 of these campuses will get libraries and universities (and the 3rd might eventually if it has free production before all theater options come available)
The first 3 to 5 cities not building campuses are responsible for commercial or harbor first and then theater. You should have 4 trade routes up in time to boost medieval faires and 2 marketplaces soon after for guilds.
Any remaining cities (or late cities founded for trade route purposes) get theater first and possibility theater only. You eventually want 7 trade routes (1 for each civ) available, but a couple can come from merchant republic or you can build some more harbors or commercial districts after the archaeologists are built in these remaining cities.
I don't bother with any wonders, including cristo and eiffel, though I recognize the tremendous value in both. I just plan to win before these become much of a factor.
The only thing I might do a little different with Gorgo from my vanilla cultural start is limit myself to 3 commercial hubs/harbors early so I can prioritize half-price acropolises in a couple more cities and build more commercial/harbors post-theaters. But I would still build commercial/harbor first in 3 cities as I want the medieval faires inspiration and I will get to medieval faires very quickly as Rome and Greece are the fastest 2 civs through the early part of the civics tree.