In my current game I have a system that is working reasonably well.
To begin with a system is either a mining or colony type, this is determined simply on the planets, if they are low enough cost to make colonising a worthwhile investment or not. Either way any new planet (unless specifically chosen for a population) starts life as an auto mining base. One planet in the system is chosen as the main holding depot and mass drivers are used to centralise all minerals here, from there mineral transports have to be used to get things back to production colonies. At some point I will place infrastructure on the colony and it will start to gain population and so the auto mines can be swapped out for standard mines, allowing the auto mines to be shipped onot the next mining target.
The method above works for just getting minerals out of the ground and leaves me with only having to manage a single fleet of mineral transports out of the system. To develop things further into production colonies though I make use of the reserve minerals function, as soon as a colony has construction factories I set a minimum limit on all minerals there. This way the colony always has enough to produce what is required, and means I can forget about having to manually check things, I simply raise this value at given points in the development. This same practice applies to all other colonies in the system as they "come online", and it gives me a continuous cycle with little micro managment.
There is always the issue of some colonies simply not having access to some mineral types, making production there impossible. to get around this you have to plan out a loop in your mass driver network that allows packets to cover every colony you want producing. Here is how I have it set up in Sol.
Callisto AM - sends packets to Russia on Earth
An out of system mineral transport drops off all mineral at Russia on Earth
Russia - sends packets to Mars
Mars - sends packets to Luna
Luna - sends packets to Venus
CMC in Sol send packets to Venus
Venus - sends packets to my capital on Earth
To start with this makes Sol a hazard for shipping lanes due to packets flying in what looks like all directions, however once things were established it meant I never had any issues with mineral supplies on any planet. In addition to this the reserve levels on these colonies allow me to blindly send a large frieghter group if I ever need a sudden influx for a large project, instead of having to specify the exact amount to load. You do need to scale up your mass driver network to keep up with your mining production for this method or it can take years before you see any results.