I am still new and learning this game. When I colonize a new plant should I build a factory first?
Generally speaking, yes.
Does having a factory, star port or even a power plant help in the building of other social queued buildings?
Of course a starport only helps build ships, not social buildings, but the other two yes.
Say this planet is only going to have banking and economical related buildings would you even build a star port?
I would argue yes, build a starport anyway, but that is a matter of opinion and your economic situation. If you're poor, don't build a starport--you're wasting 1bc/turn maintenance and you have to sink yet more bc to put the starport to use. But if you're not that poor, well--you have to build a factory anyway. Might as well invest a little bit into ships whenever your military slider is turned up.
Is it tied to population?
Production is not tied to population. Only money-making is.