Thank you very much for your answer. I apologize for not giving the version (it's G&K, still haven't gotten around to buying BNW).
So I'm guessing you want to found these cities asap? Is there a general consensus of which turn one should have their max cities up by? (assuming standard or epic pace, as these are the modes I play on).
Also, should I prioritize building settlers over other things, or go for the "buy settlers" route and use Liberty for my free/quicker settlers instead?
Not quite: It's almost always better to build NC while you have only two cities. The usual AI gold trick (now obsolete with BNW but works in G&K) involves cash building the settler for that 3rd city a few turns before NC completes to start moving it to the new location and found the turn that NC completes.
(Or if you've built GL, then normally NC is the next build while still at one city and again settler cash rushed right before and founded right after.)
Either way right after NC completes, then you expand to 4 cities as quickly as happiness & production & gold allows. This is very situation dependent on turn #; and in BNW that turn is going to be higher.
For all versions: If planning on self-building 7+ cities : This is what Liberty is designed for.
If never planning on self-building more than 4 cities: This is what Tradition is designed for.
5 self built cities can work with Tradition, but (at least in G&K) I find that 5th city must be really good to be worth it; and is often a site that if I'd known about earlier would have been my 3rd or 4th city and one of those others not built. (In this case, you cash rush the aquaduct in that 5th city right after the rest of your empire has gotten them for free)
But I find 6 self built cities to be no mans land. (Too many for Tradition & not quite enough for Liberty)
Conquering (with Tradition) : Several of the AIs cities are junk: Raze those to avoid happiness issues. Puppet initially the ones you are planning on keeping. If its a capital, you might want to annex it after it comes out of resistance, otherwise its probably best left as a puppet to keep from increasing your social policy cost.