My colonies start specializing rather early. Since I industrialize earth heavily, and invest in huge construction factory and shipyard production, other aspects need to be offloaded quite rapidly. In my last game, I started developing research worlds, which took a huge pressure off Earth's industry. I had one on Mars, and two on alpha centauri.
Because of my emphasis on what boil down to essentially Forge worlds, I need high pop centers to support massive shipbuilding and industry. It takes a very long time to get secondary worlds up to 500M+ populations, but thats a big milestone and a big step towards getting them producing.
I've been working towards a material distribution network for some time, and have begged steve a couple times for some enhancements to the Reserve Level functions such that I can set up freighters that cruise around and refill planets with minerals to the reserve level, using commands that won't get stuck (like when the fleet has none of X mineral) and require me to redo the whole network every time the cycle crashes. The idea being that I can centralize all minerals to come to a certain world, then distribute them outwards from there. Since I do want Sol to be my primary shipbuilder world, this center is usually earth, and then the distro runs go outwards from there. I see no real advantage (other than role playing) to doing ore distribution or "processing" anywhere other than Earth (or other centralized planet).
Another big one is a Refining world. I want similar network distribution commands to enable me to fill every planet to a certain fuel level with my tankers, which cycle around the empire stopping off at all the worlds to keep them topped up as necessary. However, I try to centralize the majority of my refining capacity.
Maitenence worlds I also tend to do at minor worlds periodically. Once the ships get greater than 50k tons, the maint facilities start using too much pop at the major production centers, so i offshoot them to smaller colonies focused on maitenence and (for the time being, until I get those fuel network commands (someday!)) refining capacity. I am not keen on orbital maintenance facilities, never felt I got enough bang for the buck, but once commercial shipyards (and orbital habs?) get large enough you can actually run a lot of pop-free maintenance.
For some of your other points, like administrative and military training, those don't really eat population, so I see no reason not to put them anywhere you need them/want them.