The governor-generals walkthroughs here on the forums will usually state whether you can keep the colony for yourself or if you have to give it to the nation to complete the mission. I have breezed through the walkthroughs, and I think that most of the towns you take as part of a mission have to be taken over by your nation to complete the mission. The one exception I remember is The Spanish governor-general missions, where you can take over La Vega for yourself, in an early mission, after you raid it in the name of Spain.
I have learned the hard way that there are a few things to consider if you want to capture colonies for yourself. First it helps choose the Corsair profession for your character so that you have the land assault perk, a hidden ability, which allows you to raid port towns from the jungle, and capture jungle settlements without a fort. Second, is that you need to complete the governor-generals missions in order to capture settlements for yourself. Third, in order to capture settlements with forts, you must destroy the forts cannons and then defeat the garrison.
I still am not sure whether you can capture settlements where a nations governor-general is located. It would also help to know what caliber of guns are best at destroying forts cannons. I assume larger is better, but the reload is longer, so I dont know if 100 24lb shots are better then 300-400 12lb shots.