FWIW, I pursued my first NC opening in my last game, and I expanded like crazy up until probably the Renaissance. I wasn't very focused during the Medieval era (built a LOT of buildings, which I love to do), and was behind Suleiman by around 600 points when I met him in the Renaissance era, including being 3rd in Science. But, my cities were booming, and I managed to kick into science mode fast enough for a come-from-behind victory (science).
My production was somewhat out of control in three of my cities (my 2nd, 3rd, and 5th) due in large part to the presence of 2 - 3 horses, cattle, or combo. These cities, I found, work out quite nicely as production cities, actually, as they're often surrounded by a lot of grassland with the occasional hill and/or forest to take production over the top).
I don't typically start buying a lot of buildings until I'm more or less done with horizontal expansion and pop growth starts to really bust my happiness budget. During expansion waves, I prioritize lux resources. Occasionally I'll buy a Colosseum here or there if I'm pushing up against 10
. Once My economy is going and populations are taking off, I start buying a lot more, and almost exclusively happiness buildings.
For infrastructure build order, I tend to focus on production or commerce, depending on the city, and throw in a food booster here and there if a city is stalling and I have room to grow (+ happiness)/am not currently expanding.
All in all, the NC start had me careening through techs early on, which dovetailed quite well with the rapid settling of stable-driven production centers (i.e., it felt as though tech and production were keeping pace with one another quite nicely). I was definitely maxing out happiness at many points, but kept things under control via a CS alliance and lux trading. If I were a more efficient, careful player (for instance, I plopped a third city while in the middle of building the NC
), I think the synergy would've been even stronger. I also tend to favor fun over efficiency (weird strategies like building buffer colonies on the far side of choke points, building tons of buildings without enough thought about their true benefits, settling a Conquistador simply because I wanted to see it happen
, etc), which probably killed my momentum in the middle ages.
As I mentioned above, I play on Prince, although I think I need to move back up to King again (moved down after Nov. patch).