In 6.0+ bouys last indefinitely. That is, any missile without an engine.
A sensor bouy is just a sensor+reactor of whatever size your bouy launcher is. Larger is of course better, but more expensive (though bouys are generally so cheap it doesn't matter), and requires more space for launcher and magazine. I suggest different designs for EM, thermal, and active. The most use is as an early warning system. A thermal/active sensor on an inbound JP will spot any ships coming through, or it'll die and warn you by absence. A tactic I've used is to stick a size 1 launcher and a few magazines on my gravsurvey ships. They can then drop geosurvey bouys on interesting looking planets, and EWS on JPs, without requiring a dedicated ship.
A mine is a sensor and a bunch of submunitions with the same sensor. Mnes are mostly used for defending JPs. Because the enemy usually won't have any missile defense working when they're shot, the submunitions can have more warhead and less armor tan a typical missile. Both mine and submunitions tend to be large, in order to minimize the space used for the sensors, and again, because they're unlikely to get shot down. The mine sensor should be a bit more than the enemy's squad jump range. The submunitions sensor can be smaller.
The only mine I've really ever used looked like this:
