A few unconnected thoughts:
Late game: have the best computers - shooting first is a huge advantage with advanced beam weapons.
Always be clear about your objectives for the battle - do or die; or inflict as much damage as possible with minimal / zero losses. Be prepared to retreat and sacrifice undefendable colonies - better to lose just a colony rather than a colony + fleet.
If you have Class 3 or better shields, make sure the strongest side of your shields faces the enemy at the end of each turn.
If you have good mobility:
- * Move toward the outer edges of the enemy formation, so it's hard for them to concentrate fire on 1 ship. Particularly effective if you have good shields and manouevre as above.
*If they fire tons of missiles or fighters and you have mainly beams: (a) move just close enough to hit their ships with HV beams; (b) use normal weapons to reduce the missiles / fighters; move away but ensure that at the end of the move your shipsd are at an angle where PD weapons can hit the missiles / fighters. The rationale is that you want to last until the enemy are out of missiles / fighters, then your beam weapons can strike withj impunity. Works best if you're attacking an enemy system, as the enemy won't be so happy to retreat.
If you have mainly missiles and the enemy does the "fall back and thin them out" manoeuvre, move forward without firing, so they don't have the space and time for "fall back and thin them out" and you have ammo left.
With missiles, use 3 groups: fast, armoured to absorb as much PD firepower as possible; heavy hitters to take down shields; EMG for quick kills. In this time your manoeuvres and firing so that the missiles arrive in that order.
If torpedoes (fire every 2 turns) are your main weapons, dance your ships back and forwards, and keep your strongest shield side towards the enemy at the end of each turn.
And, as you said, pick your targets. Especially concentrate fire on as few enemy ships as possible if they're too tough for 1 ship to kill themn instantly. But don't over-kill enemy ships if using missiles (not a peroblem with beams) - use the excess firepower to start weakening another target (or perhaps kill it if not tough or several o fyour ships have sdpare firepower). That means: (a) your weapons should be spread over as many slots as possible, to give flexibility; (b) turn "off" missile / torpedo slots that should not fire on the current target.