Automines are more expensive and require more minerals to build. If a planet has minerals you want and is colonizable, put some people there and use regular mines. It only takes 50k people to run a mine, so a couple million will cover your personnel needs for the first decade or two. Automines are for uninhabitable locations, although they will work anywhere.
Moving minerals in the same system is best done by using mass drivers. A mass driver will launch 5000 tons/year to the target of your choice; it will be a while before you need more than one launcher. Make sure you have a mass driver on the recieving end as well. Otherwise, large rocks are crashing into the target at very high speeds, which is bad for the environment and those who live in it.
This almost happened to me in my game and I didn't stick with it to see what would happen:
Say you launch a mineral packet at a planet and while the packet is en route a freighter comes by and packs up the mass driver. Will the mineral packet actually cause damage to the target colony?