Smoelf describes the easiest solution and the one that most players start with. If you're colonizing all the bodies in Sol, then you'll soon have nice, if smallish, colonies near Earth that can share the load to an extent. Usually people create single-purpose colonies, so one planet does research, one does shipbuilding, one does construction and so on, depending on population availability.
Outside of Sol, the easiest method is to have a central gathering colony in a system and then have mining colonies feed minerals to it via mass drivers. Freighters then move those minerals from system to system. Initially everything is brought to Earth, then later you might have those central colonies turn into manufacturing locations. Eventually you'll have so many labs and factories and shipyards that no single colony can handle them (or you followed the advice in the first paragraph and even Sol is running out of workers) so you need to start sending installations elsewhere.
As for sectors, none of my games have lasted long enough to make sectors very important so I can't really give advice there. I just build enough Sector Command levels on Earth to get bonuses around it and that's that.