Please don't use TL as a shorthand for clarity's sake.
Sir, yes, sir!
(https://vintage.ponychan.net/chan/arch/src/131002311820.png)
Almost forget to Say my own words: I always diversify weapons, so there are many leaders in each role. However, if I had to choose single most-favorite gun, that would be a graviton beam. Range+efficiency+kinetic. Low DPS, you say? Use MORE graviton beams. The only weakness - it would never kill anyone. :-\
Based on my playstyle, well...
Ballistic
Spoiler
Small: Vulcan
High rate of fire can shred missiles and torpedoes, more so with point defense AI or Advanced Countermeasures skill. Its short range is its drawback, but can be alleviated with integrated targeting unit. Deadly to fighters that got too close, and any ship with shields and armor down.
Medium: Hypervelocity Driver/ Dual-Flak
Long range at 1000 su, can reliably deliver hard flux against shields, and punishes anyone tanking with armor with EMP despite dealing not as reliably as energy weapons. Dual-Flak reliably destroys what would have been a dangerous lone piranha wing, or at the least a lot of annihilator rockets. Burst PD lasers cannot deal with those things.
Large: Hephaestus Assault Gun
A compromise between fire rate, accuracy, and flux, and can bust armor reliably if the Hellbore misses against smaller targets. As much as I like Mjolnir's energy damage and EMP, its flux demands require some compromises but not as much as a Storm Needler's.
Energy
Spoiler
Small: LR PD Laser/Antimatter blaster/Ion Cannon
LR PD Lasers have the range to at least take down the sabot missiles before they detonate, but needs point defense AI to deal with flares and prevent wasting time selecting targets. Antimatter blasters are the typical weapon of choice for alpha-strike designs, usually with phase ships since they usually run out of time before they run out of ammo. Ion Cannon is short range, but in the right ship, it can also disable weapons at high flux to give the shields breathing room.
Medium: Pulse Laser/Phase Lance/Ion Beam
Pulse Laser consistently builds hard flux while being forgiving to flux use unlike the heavy blaster. Phase Lance is usually better in player hands, since the spike damage is better use when shields are down or trying to sneak damage past shield cover. Ion Beam has 1000 su, and sacrifices dealing significant damage for significantly annoying ships under heavy flux pressure or lacking shields with constant EMP.
Large: Tachyon Lance/Plasma Cannon
Longer range than a phase lance, charges longer than a phase lance, hits harder than a phase lance, and delivers EMP unlike the phase lance. Plasma Cannon consistently fires damage over the Autopulse Laser, and can build flux more reliably.
Missile:
Spoiler
Small: Salamander
EMP missile that refills in battle. It can't destroy like harpoons or any torpedo or deliver flux spikes like sabots, but it ensures a ship stays as a missile threat. Leave the smaller sabots and torpedoes to fighters.
Medium: Harpoon/Sabot/Reaper
Harpoon and Sabot has more ammo as a medium, delivering payloads in longer fights. Reapers are great at alpha strikes, especially in the hands of Dominator or Doom as a salvo is more likely to hit unless the enemy fleet has significant point defense.
Large: Locust/Hurricane
Locust missiles can flood PD screens lacking flak, destroy bombs and fighters through volume, and can be used to finish off overloaded breached ships with extreme DPS per salvo. Hurricanes are second best as it quickly destroys armor or more difficult to dodge when the smaller missiles are fired as a spread.
For breaking shields, the important thing is efficiency. Offenses and defense are coupled here in the sense that taking shield damage reduces your ability to fire your weapons because you have less free flux capacity, and vice versa, dealing damage to enemy shields reduces their ability to shoot back. You want to raise more flux in the enemies ship than in your own meaning the ratio of damage dealt to the enemy vs flux raised in your own ship is super important. Kinetics deal double damage to shields so they effectively have double efficiency which is very strong, but they deal very reduced damage to armor meaning they won't be able to finish things off. When I'm choosing kinetics, I like to choose the highest possible efficiency.
Spoiler
for small kinetics:
the big choice is between railgun and light needlers. Needlers are more efficient but railgun have higher dps and better armor penetration. They're very close in value.
The light dual auto cannon is my budget choice.
The light dual machine gun also has good efficiency but very poor range. It can be useful on safety overrides (SO) ships but otherwise it is relegated to PD.
for medium kinetics:
Heavy needlers are a clear best for me with the highest dps and best efficiency, the only downside is the very high OP cost, but I consider that 100% worthwhile.
The heavy auto cannon: an honorable mention for a good medium kinetic, it will get the job done and I use it where I don't have enough needlers, or where I am very tight on OP.
The heavy machine gun is a decent SO kinetic option but it has too little range to be good on normal ships as an assault weapon.
Another honorable mention to the hyper velocity driver. It trades efficiency and dps for range. You can make some fun sniper load outs with it but its not a great general purpose weapon IMO unless you're looking to match the 1000 range with all your other weapons.
For large kinetics: I'm not a huge fan of any of them. The Mark IX and the storm needler are both not bad, but I prefer to just get my kinetic damage from medium/small slots and use the large slots for anti armor damage.
Storm needler: a good choice if you want to crush a capital ships shields, but it costs so much flux to fire that it really doesn't work well on most ships with large ballistic slots.
The Mark IX: like a large heavy auto cannon, it gets the job done but it's really not exceptional in any way. I frequently use it to fill slots with decent damage but I'm not super excited about using it.
The gauss cannon: a very specialized sniper weapon that is fairly inefficient but has the longest range in the game. You have to build the ship to use it, you can't just throw it in any slot, but it's good when used properly.
For breaking armor the important thing is the damage per shot (the damage a single projectile does) and the dps to a lesser extent. The armor damage reduction formula basically reduces the damage more if the damage per shot is less. HE weapons deal double damage to armor making them both more efficient and better at actually penetrating the armor, but energy weapons also generally have high damage per shot. HE weapons also deal half damage to shields making them very bad at shield breaking. Generally you use them as finisher type weapons. I'll just talk about ballistic HE weapons here and then I'll talk about energy weapons later.
Spoiler
Large HE:
The hellebore: the capital crusher. It has an insanely high damage/shot and good efficiency. The downside is that it rarely will hit anything smaller than a cruiser because the shot speed is slow and it has lower dps. I think it's a very good option for dealing with heavy armor and keeping flux cost down, but it's not very good vs smaller ships making it a more of a budget/niche weapon.
Hephaestus assault gun (HAG): has much lower damage per shot but can hit destroyers and also has much higher raw dps. It will be worse against capital ships and better against everything else. I think it's a good all around gun, and probably works well as a 'default' large weapon. I frequently pair it with the Mark IX if I have two large slots to fill.
Devastator: a PD hybrid, but it is somewhat inconsistent at both dealing HE damage and killing fighters/missiles.
Medium HE:
The big choice is between the heavy mauler and heavy mortar. The Mauler has better armor penetration and range but worse DPS and OP cost. I think I often choose the mortar for smaller ships because it costs less OP, but the mauler has much better range which can be very good as well.
The assault chain gun is mostly limited to SO ships or maybe capitals because of its super high flux cost.
I don't think small HE is any good because the damage per shot is too low. The railgun will always be better IMO.
Energy weapons don't get any bonuses to shields or armor making them more generalist and generally a little less effective, but high tech ships have more dissipation and capacity which sort of compensates. Usually I think of energy weapons as more anti-armor leaning than anti shield, but they can do both.
Spoiler
Large:
Plasma cannon: the king of large energy for me. It has very good armor penetration, very high dps, and still deals a respectable amount of hard flux damage to shields. The main downside is the enormous flux cost but all of the ships with large energy slots (paragon, odyssey and apogee) have high flux dissipation and can build around it. It doesn't have very good efficiency so it's important to maximize your dissipation when using it.
Tach lance: a close second for me, It's very much an anti-armor weapon with large burst damage but a little lower dps. I use it on the paragon and also sometimes on the sunder. The fact that it is a beam and deals soft flux is a significant downside for me though.
Auto-pulse laser: the anti-shield weapon of large energy. It has noticeably better efficiency than any other energy weapon. The main downside is that it runs out of charges. It sort of requires extended magazines to be good, but overall It's a solid choice, particularly for the AI.
HIL: a support weapon, but it does a huge amount of damage. My main problem with it is that most of the ships than can use it don't have access to weapons that set it up well. If you are fighting pirates with crapy shields it will tear through everything, but if you are fighting remnants with good shields it will struggle.
The Mjolnir cannon is actually energy damage as well even though it is a ballistic weapon. It's something like the plasma cannon with slightly worse anti-armor capability and slightly worse efficiency. I don't use it very often because most of the ships that can mount it don't have a ton of dissipation and also have access to kinetic and HE damage which is more effective.
medium:
the heavy blaster: a HE weapon disguised as an energy weapon. It costs an absurd amount of flux to fire and your loadout has to be built to support it, but it will crush armor. Some ships like the aurora can bully smaller ships shields with it but you will always be at a disadvantage trying to crack shields with it. Its powerful but a bit niche because of the flux requirements.
The pulse laser: the mediocre option. It deals hard flux and has decent dps but has poor range, efficiency and damage/shot. I try to avoid using it on most ships, but it's really the only hard flux that some of the high tech frigates can use.
The phase lance is a baby tach lance, but it costs too much flux to fire for my taste. It's another anti-armor leaning energy weapon since it only deals soft flux. I will use it sometime, but its not my favorite.
Grav beam: the filler. It doesn't cost much flux to fire it provides decent shield pressure so I usually use it to fill slots on ships that don't have much dissipation to spare. It's a support weapon so ships need other things to be effective but it definitely helps finish things off with 1000 range and perfect accuracy as well.
small:
tac laser: another support beam similar to the grav in many respects. A good filler but it does cost a decent bit of flux to fire.
IR pulse laser: i think its pretty bad because of terrible range and low damage, but its the only small hard flux option
Anti-matter blaster: It's basically a missile that costs flux to fire and has no range. It does a lot of damage but the AI is terrible at using it so I consider it pretty niche.
For PD weapons, there are two major targets: missiles and fighters. Some weapons are good at one and some are good at another.
Spoiler
Flak and vulcans are the best anti missile weapons and burst PD perform decently as well. Vs fighters, the kinetic PD like light/heavy machine guns are good choices and burst PD is also decent. The PD laser/ LRDP laser sort of work but I usually go for a few burst pd rather than a lot of pd lasers. They just don't do enough damage to deal with big swarms of missiles and they don't kill fighter quickly wither. I'll use them to fill slots of I have the OP and dissipation to spare.
Missiles are basically for huge zero flux alpha damage with a few exceptions.
Spoiler
For large missiles, I usually use locusts as a finisher when ships are running away or just for supplemental dps vs hull. The other large missiles weapons just don't have that much ammo.
For mediums and smalls, I usually use either sabots or reapers. Harpoons are also decent. Sabots are probably the strongest missiles but are only good for cracking shields.