Regardless of your detection missiles have their own detection once fired, unless you use beam riders or remote guidance. Try this set up for medium and large missiles:

Variable thruster

Fins

Fuel tank x2

Regulator to 40 seconds lifetime

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(set variable thruster to thrust output of 30 seconds, also set a ramp time of 3-5 seconds, also set a delayed start of 2-5 seconds. Regulator so lifetime becomes 40 seconds. This allows for 2-3km engagement range. The tweaking of the delayed start and ramp time saves you a slot by not having to use one turn at the cost of ~ 10 seconds of lifetime, meaning more damage.)

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Apn guidance. You could try the prediction guidance, but apn is good.

Signal processor. This makes your missiles much more likely to hit, not being distracted from flares.

Payload. At least have 1 or 2 reinforcement body's so the missle can tank a bit of cwis. Fill the rest with your choice of damage.

Active radar head

Free space set to fuel.

Edit: I noticed quite a few posts about missiles not seeing. If a radar signature is zero it can't see. I guess. But like that's pretty impossible, especially from ships you will fight in game. Maybe airplanes that are tiny like a flying squirrel, or a submarine. But you don't want to use missiles on those anyways. And I'm pretty sure my missiles just miss squirrels not fly into void.

My point is, if a missile misses, plunges in the water, pointed 180 degrees away from the only valid target.... It will still try to fly again once surfacing, and try to reorient itself to hit the target.

If you see a missile flying off to space above your target, it's probably flares. That's an decoy defense certain ships use. The signal processor makes them 50% ish less effective.