Manual Mines: cost 120 corundium, require population to work. You usually want to use these if possible because they are cheap, but population is often a limiting factor (either a body is difficult to colonize, or you simply can't move people fast enough).
Automated Mines: cost 240 corundium, require no population to work. These are in terms of resource efficiency the worst choice, but they will always work in every situation which often makes them a necessary evil.
Orbital Mining Modules: cost 120 corundium (plus a bit for ship structure, etc.), require no population, but can only operate on small bodies. These are actually the best possible mine you could use (same cost as manned, no population requirement) but are only usable on a limited set of bodies so sadly you cannot use them for everything.
For an effective economy you will need to build all of these in most cases. Players often want to avoid Automines but they offer a lot of usefulness in avoiding a mineral crunch when your colonization fleets are not moving people to manned mining worlds as quickly as your shipyards chew through your duranium reserves.