For late game when I have all the blueprints and can build whatever.
Small Ballistic: Light Dual Machine Gun, Light Assault Gun, Light Needler.
The Light Dual Machine Gun does it all in terms of point defence and close range anti-shield work. Shielded fighters beware! Vulcans are great for point defence vs missiles but only ever take down fighters with sustained fire. DLMG's work nicely as a close range shield killer for a fantastically low cost. The Light Assault Gun is decent for what it does, although a little flux heavy. The Light Needler doesn't have the range of the railgun, but does decently in bursts against small foes. Me liking it might just be a phase however as I usually don't get to use them.
Medium Ballistic: Heavy Machine Gun, Heavy Mauler, Heavy Needler.
The Heavy Machine Gun can be hard to find, but are kinetic gods. They work as PD too! The Heavy Mauler is a powerful artillery cannon that is fantastic even in capital ship fights for it's sheer range. The Heavy Needler doesn't have the range advantage and does basically nothing against armoured foes, but other then that it's fantastic for downing shields.
Large Ballistic: Hellbore Cannon, Storm Needler.
I love the Hellbore Cannon because it does exactly what it's supposed to do for a cheap cost. It deletes armour. The Storm Needler like the rest doesn't have the range advantage, bit it's shield stripping power is incredible.
Small Energy: LR PD Laser, Antimatter Blaster.
Hard to choose for small energy as I often don't have a chance to use them without delegating them all to point defence. Most high tech ships have at least one medium slot or are torpedo boats. The LR PD Laser is cheap, plentiful and has fantastic range. Damage per second is rough however. The Antimatter Blaster is a missile weapon and a guilty pleasure to put where it doesn't belong. I once had two on a conquest.
Medium Energy: Graviton Beam
I find energy weapons hard but that might be because I don't often know what I am doing with them. But one thing I know is that the Graviton Beam is a must for ships with any energy that that does soft flux. They can't kill armour, but just about every other energy weapon can!
Large Energy: Autopulse Laser, High Intensity Laser.
The Autopulse Laser is, in my opinion, the best overall hard flux energy large weapon. It's the gun that let's Paragons duel Radients and live. The High Intensity Laser is fantastic when mounted on sunders for their supporting fire-power in capital fights. While other ships tank damage and deal with shields, the sunders kill any exposed targets with their pin point laser beams. Great when used in support of anti shield kinetics.
Small Missile: Harpoon MRM, Sabot SRM
The Harpoon MRM is the general purpose missile that does it all. Great when massed with eccms. The Sabot SRM breaks the game by provding massive burst kinetic damage that is very hard to avoid for no flux cost to use.
Medium Missile: Harpoon MRM Pod, Sabot SRM Pod
Same as above, but more of them.
Large Missile: Locust SRM Launcher
Ravenous swarm missiles that devour entire flight wings and smaller ships alike. Great fun and easy enough for the AI to use.