Ok I think that each Country would rule itself as long as it adhered to certain standards. It would mostly likely be like the UN but with teeth. As soon as a politician steps out of line or becomes corrupt starfleet security beam in and arrest them end of. People like Hitler, Sadam Hussian, Assador and all the other useless pieces of scum we have now days running things would have been removed from there position before they could hurt anyone.
As for economy I think It would be a Socialism/ Capitalist hybrid with a heavy leaning toward Socialism.
I think everyone Guaranteed:
Basic Clean Water
But if you want a better house or a tastier food, holadeck time or a nice holiday you have to get a job and earn energy credits.
One things for certain there is no huge poor/ rich divide. There is enough work for everyone. And everyone gets the same top quality healthcare and education.