Wherever You Go, There You Are
With no certain future, and no purpose other than to prevail
I'll cover for both beams and seekers here.
First, the map answers part of your question. The map has your ship, your future position markers and your target's markers.
Will you be closer or farther away next segment?
If closer, will the change in range favor you over your opponent?
Will you be able to penetrate the armor on the opponent's ship? If so, by how much? As a rule of thumb, you want to get at least 5-7 points past the skin armor value to deal with the intial armor soak and component armor on the system hit. If you're doing so much damage you'll blast through the ship like a drill bit hitting butter, you may want to not aggregate damage.
If you can't penetrate the armor you're facing, look for a shallow angle shot, or snipe at a weapon mount, or the engine or the mast.
For seeking weapons, the "no calculation" rule of thumb is this:
If you're closing on each other, ALWAYS launch seekers if he's your primary target.
If you're moving away from each other, it's probably not worth the resources spent.
If you're moving tangentally to each other, seeking weapon use is conditional - do you want to encourage him to move in one direction? Can you provide enough saturation to guarantee a hit? Or can you provide him an ugly choice - thrust in the direction he's facing and hit seekers, or evade seekers on the golden path you've laid for him that forces him into exposing a more vulnerable part of his ship to beams?
Most seekers get either shot down or avoided. The ones that hit are usually quite telling...and sometimes, having them shot down or avoided is just as important as having them hit, since shooting them down costs power (unless ZDCMs are used) and avoiding them costs fuel, runs the risk of engine damage, or can force someone to pivot weapons out of arc for the evasion, or can force tactical separations.
That last one is quite useful. If you have two ships trying to maintain formation, you can separate them easily with seekers -- make two spreads that give evasion directions 180 degrees apart. Now, if one evades, and the other maintains formation, the second ship has to fly into the teeth of a seeking weapon salvo. If both evade, the formation breaks up...even if no seekers hit, you've achieved something.
Even seekers that won't penetrate the facing armor have a use - they can force the ship to keep its good armor pointed at them, preventing a pivot!
When it comes to avoiding seekers, James Brown has two pieces of advice:
1: The worst time to have seekers launched at you is just after you've started a pivot.
2: The second worst time is just after you've turned your engine off because of the two segment delay on re-ignition.
James recommends that you save your pivots until you absolutely need them, and accept the risk of melting your engine off, thrusting nigh unto constantly....and James is very hard to hit with seekers. Of course, he also burns more fuel and ends up with truly improbable vectors at times, but that's better than getting cored like an apple by a 200 kilo shell.
If the seeker salvo is making him do what you want him to do, it's worth launching. Figuring out if it will do that requires experimentation.
“Weniger Denken, Tuend!” (Less Thinking, Do It!).” is a very important concept in playing AV:T - you're playing a flight simulator more than you're watching a space battle unfold from God's Own Helicopter.
It's very easy to worry about what the rules are doing and try to iteratively predict where everything will be for a full turn - it's a habit that has a reward mechanism built in from other games, and it's a habit that will give you brain leakage in AV:T.
Sit back, fly by the seat of your pants. You'll learn more playing three games sloppy and going "Ooooh, OK, that didn't work..." than you will from trying to spend the same time playing one game perfectly. You'll definitely have more fun...