Mines today are not always of the static spiky variety of old. As was mentioned, Captor mines are probably the best solution to seed a system with.
A solar power or a small fission reactor like we use today on satellites and probes would be perfect. The missile(s) power supply would be kept for the missile.
IMTU I have network mining operations that happened in a few systems in wartime, and are now a fun hazard for PC's who want to go to the deserted (hopefully) worlds for looting and such. The mines in both cases are networked with sensor probes drifting around waiting for the right kind of neutrino sources to show up. Provided the source (radio transmissions, and other lower tech energy sources also sometimes work) matches the right signature and the vector is active then the nearest mines to the target go active.
Most of the mines are either one-shot bomb-pumped laser missiles or bay-weapon sized "torpedoes" (in my game's vernacular). They can either be in a three-shot pod (about the size of a triple turret), or the sneakier ones are drilled into asteroids if the system has a belt of those between the gas giant and the primary world. The second type is impossible to spot before launch, but the first type can be spotted by a good sensor officer and the right suite on the ship. Scout ships are naturally better than the other kinds for this given their sensor suites, and their smaller size tends to mean they are harder to hit while evading.
Essentially, I use the same rules for mine attacks and defenses as for ships and small craft, with the mines treated as missiles and the mine launchers and sensor probes as small craft.
The whole point behind them is cheap area denial and increasing the caution of your opponent which can lead to him taking longer to make that strike on the world so you have more time to do something to stop him. I mean, spaces is kinda big and there is no way you could encircle a world with the things and get you money's worth. The enemy would just punch a hole and dive through.
But if the little buggers are scattered around with a bit of tactical thought then they can be a real PIA to an attacking fleet.
Accordingly the sensor probes are not much more than a self-powered passive sensor system with a small maneuvering drive and an ECM package. The torpedo pods are just launchers with just enough power and commo gear to stay in touch with the network. Space them out right and they just hand off the signal to each other with sensor probes every few mine pods. The sensor detects a ship with its passive sensors systems, bursts a signal to the pods nearest to the target and the missiles go active on their own. Makes the sensor probe harder to find, too.
For variety mad-scientist style you could even have a few asteroids drifting around that have a spinal PAW or something buried in them with a one-shot capacitor load. Network the system to track the target - hit the target with the PAWs from various angles. Again, planning is crucial on where to place the PAW-roid mines. I think missiles are the most logical choice anyway: cheap, simple, self-powered and self-guiding once launched. Mines should be disposable, after all.