I can't remember my starting build order exactly, it was a little weird. It was something like Worker Worker Settler Water Mill Worker Warrior Settler Settler, with 1 or 2 bought warriors along the way.
I did build happiness buildings that game, along with getting Theocracy.
I built a lot of early aqueducts, which helped me to eventually get 4 size 12+ (I think 2nd city reached 18!) cities, all with superb production. 2 of them were making 1 turn musketeers.
The land was very hilly. The 4-5 mines/workshops/pastures/golden age seems accurate. I had 4 cities that were all "excellent caliber". At the end there, I had my 2nd happiness golden age, stacked with Piety golden age, stacked with Taj Mahal [Great Engineer] for a grand total of 36 turns of golden age.
I managed to snipe a rival's Great Scientist with an amphibious attack from a Spearman immediately after getting Astronomy, which slowed down his Rifling or Navigation tech.
I was on my own continent, and had so many hammers I built about every wonder that was not in the Education tree while I was waiting for Astronomy (including Chichen Itza, Notre Dame, etc).
I did not build NC until turn 65 or so. Still managed ok beakers, due to the early aqueducts and population.
I built Collos/Circus Maximus as well as Notre Dame and Theocracy, which enabled me to build 4 new cities without worrying about impeding growth.
My first medieval techs were Currency, then Engineering (love aqueducts!), then Civil Service, then Metal Casting, then Education. Aqueducts are equivalent to +66% growth, so the earlier you can get them, the better for hammers. Currency first was a necessity because my Civ had about 70 MFG and 28 GNP sometime around turn 50-60, causing my maintenance costs to skyrocket
I would have preferred Metal Casting first, but my late NC caused me to not have time to squeeze it in.
One of the late cities was actually a Seaport city, rather than an ICS university city. It immediately upon founding bought a Seaport, a Lighthouse, and an Aqueduct, to make immediate use of the 6 Fish/1 Pearls, that would have been the capitals had I not moved it away from the coast (I preferred the hills and sheep for early game, instead of fish which do not help you immediately. Its production rose quite fast, as the 5F/2H fish tiles are wonderful
The land was... basically imagine the perfect land.
Capital had 7 sheep, and my 2nd city (~10 tiles away) had a different 7 or so sheep. Both also were built on hills by rivers for the Water Mill and early production. The other two cities had riverside farms and a ton of hills. The 5th initial city was placed in Tundra on Furs, and did not build an aqueduct or ever get beyond size 6. It used some hills and deer.