Some weapon ideas I very much likey;
SD Beams - Very underrated, provide some pretty intense shield regen while doing decent shield dmg for their size, awesome defensive option for head to heads or for a smaller vessel to outregen swarmer rounds, can be slaved with anything but no effects. Can't be used by AI
Missile - Beam - Pierce - Put this in a big waffle pattern with shots layered back to back, insanely penetrative, turn clusters of smaller missiles (so swarmers also but ehh, i dont like em as much) into a nightmare for your opponent, pierce has a large armor damage malus, and waffle patterns are inherently low dps for size, but with a large grid it simply melts through armor through repetitive pierce hits (including baffled armor), this makes a good one shot weapon against lowly armored/smaller ships, but some alt shield damage support is needed.
Beam - Beam - Ion - Awesome burst per block, can't be interrupted like missile damage and gains full benefit from Ion effect (missiles only gain 50% of the bonus shield damage at best), several of these forward mounted on turrets set to select target is some top tier passive shield shredding.
Cannon - Beam - Overdrive - For pretty much the same reason as above, AI are decent little snipers so long as you handle the range for them, great for smaller railgun type turrets, huge shield damage with solid penetration.
Beam - Missile (~20-25% linkage no more no less) - Punch - Godlike block damage given enough space to benefit from punch & as large a waffle grid as possible (I would say at least a 10-15k block weapon system), requires close range, low missile slave linkage gives an extra beam without sacrificing much damage & keeping a relatively tight firing grid, looks really flashy and can punch huge holes.
Missile - Pulse - Ion - Near useless at long range unless your target is very slow to take off or has no AMS/low thrust, but makes an insane shield popper for smaller ships in the heavy fighter to light cruiser range, a rush into close range followed by a hit from one of these from a small/fast ship with a higher power cap will make ships even 10x your size or more shit a brick.
Cannon - Beam - Punch - Keep a tight circular grid pattern with shots also layered back to back a few times, use this for hunting down the rail connectors and computers on well armored targets, most useful if you're mobile enough to stay close despite having great range, could definitely be subbed for more computers with pulse instead of beam.
Cannon/Beam - Cannon - Overdrive - Swarmy drones with just this, in single outputs, is really really really brutal, with good thrust small ships chase very well, aim well with one/few outputs and gain a huge bonus to shields via overdrive while retaining decent block damage.
Cannon - Cannon - Stop/Pull/Push - pure number of hits seems to do much better on momentum effects than the size of the hit, so a huge cheap wafflegrid of these suits a double purpose of CCing your opponent while being useable as a forward anti missile system.