I don't think going wide and take opponents cities is really the same, for a peaceful wide start i usually scout a lot, then drop 3/4 city, then there a happiness break where i wait for key techs to be researched , all techs related to lux improvements plus trapping (circus is upkeep free) plus construction (coliseums) and the wheel for city connections, sometime during this period i'll have to stop city growth in order to keep the empire happy, i try to build the NC in one of my towns at this time.
This is the hardest time for you, you need to try and keep your science high without too much citizen, spread your religion because it can provide happiness per city (it's what your looking for instead of global happiness) build international trade routes because they provide science and gold or sometimes use hammer local trade routes to get your key buildings quick in newly founded cities.
I'll then beeline education and astronomy for science and scouting (you also need compass for ports that provide city connection), and after, while your looking for new spots with your caravels you need to reach physics (notre dame is good but i don't get it often on immortal) and printing press for zoos.
I usually have a very small army during the first 150 turns to keep gold coming, you also need CS happiness, so going patronage is probably a must.
After turn 150 it will probably be a lot easier to found new cities, and that only then that i really become wide (going over 6 cities).
Maybe it's not the best way to go wide, but i can't keep science and happiness if i try to plant too many cities before turn 100, you also need to focus more on production than growth in the beginning.
I play low profile with IA in the beginning as i feel my empire is a lot more fragile this way than if i open tradition, try to not upset them with town too close from them.
Early gold should go for workers(you'll need a lot of them), settlers and tiles purchases (you need lux ASAP), you can also consider planting settlers right on top of a lux if in a hurry.