I have found that 2 works best, 1 leaves you short on cash for CS bribes,and 3 ups the policy costs too much. Bear in mind if you are playing a culture you while be filling out the patronage tree so will get a substantial science boost from your city states (at some points over half my research was from CS in recent games) . And with all the extra resources from your CS, you can sell most of what you have in your own lands.
And you want your second city up as soon as you have the funds for the settler. Ideally you want to be able to build one of the Theology/Education wonders in it.
The current HOF Beta 5 is a cultural game, you might want to check that out for more discussion.