Will freemen be the best pop type?

[KaiserJohan]

Slaves are extremely important because, without modifiers, every 15 slave pops produce one extra Trade Goods and if present in Capital they give very strong empire-wide modifiers. Sadly, you cannot enslave your own people...

Also as others have mentioned, the more your Civilization rises the unhappier the Tribesmen become, so as Rome for example you'd want to promote all of them eventually. No barbarians in the Eternal City!

 

[Trin Tragula]

Do Citizens have an effect on the civilization value of a province? Faster growth perhaps? Higher cap? Loyalty bonus

It is the other way around. Citizen happiness is very closely tied to the civilization level of the city in which they reside.
As you know happiness both impacts productivity and unrest, so citizen in low civilization cities will not only not generate any research or commerce for you, they will also generate unrest in the city.