Do ships need to detect enemies on their own sensors to be able to shoot them? Or is it possible to create a sensor-cruiser with powerful sensors that escorts a dozen "blind" gunships?
Also, does the "missile drone" thing need its own sensors or can it again rely on Earth's sensors?
Finally, would making proximity-mines (2-stage probe with a long lifetime, sensors, and releases missiles once it detects ships) be a cost-effective way to defend jump points far away from any colony?
A target needs to be detected by active sensors to shoot at it, but it doesn't have to be the active sensors of the ship doing the shooting. A single dedicated sensor ship will therefor work, but if you lose all the sensor ships none of the other ships can fire.
The drone should probably rely on Earth based sensors, so it can correct its course in flight (it will probably take hours or days to reach a warp point from a planetary launch, during which the enemy ship may move), which means you'll need a PDC with extremely powerful active sensors. Again, though, you can have one sensor PDC and leave it out of the launcher PDCs (though the launcher PDCs will need a missile fire control 1/3rd the size of the dedicated active sensor).
Mines are doable, but not everyone is a fan of them. For one thing, they don't split targets; if you put 100 mines on a jump point and a small scout comes through, they'll all launch their missiles at that scout. If there's no colony in the system, I prefer to just drop a bunch of deep space tracking systems on some rock near the jump point back towards my colony, to give me warning if something enters the system.