My goal is to list and describe all the weapons in transcendance that don't require you to aim.
Omni laser cannon: Level III. 3 MW. The freighter starts out with this weapon, and you can often buy one in the stores of the first few systems. Being a laser, it can be stregthened by a laser amplifier (adds 10%) or a laser collimator (Adds 100% to all installed lasers). All lasers have a range of 60 LS.
Omni Turbolaser Cannon: Level IV. 7 MW. A slightly better version of the OLC, this can usually be found in a store, and some weapons shops have a function to install one for a price.
Omni Particle Cannon: level V. 20 MW. You may first find this in stores at st. k's or a few systems after. Particle weapons have a range of 120 LS (I think).
Akan 600 Turret: level VI. 6 MW. This is the first ammo-based Omni weapon. You may find the Akan 600 in a pre-st k's shop, particularly Black market shops, but it's a military weapon so you most likely need a military ID before you can use it. Though there is a danger of running out of ammo, The ranx ships use this ammo, so they are basically an infinite source of it. Other than the ammo requirement, this weapon is powerful enough to use throughout the game.
Omni Tev 9: Level VII. 40 MW. This is a fairly powerful energy weapon. Though you will mostly buy these from high level shops (5-10 systems past st.K's.) you can sometimes (very rarely) loot a working omni tev 9 from a kobol gunship. This gun has a range of 90 LS (I think)
Omni Thermo Cannon: level VIII. 8 MW. This is the other ammo based Omni. The OTC is very powerful - so powerful that it is capable of blowing up wrecks. The ammo for this weapon is rare, though. There is a late-game method for creating more ammo, but that would be a spoiler

Omni Ion Blaster: level IX. 120 MW. A powerful late game weapon, the OIB delivers enough power to blow up almost anything in the game. Some enemies, though, are immune or near-immune to Ion damage, so having a backup weapon is wise.
IM90 Multi target Blaster: Level X. 300 MW. The IM90 is essentially three Omni ion blasters that fire simultaneously and independantly. That is , if there are three enemies present and you hit the spacebar, each enemy will be hit with an ion blast. if there is one enemy or no enemies present, the three beams fire in a 15 degree spread. This means that it is possible to hit one enemy with all three blasts, and that's enough firepower to kill just about anything quickly. I have blown up teraton stations and defeated the Iocrym with the IM90.
edited to add:
Ares lightning Turret: Level VIII. 100 mw. The lightening turret fires a lightning gun beam, but twice as fast and auto-aiming. But the weapon can only fire for a few seconds (there is a "temperature bar" on the screen while it is firing), after which it must cool down for a while. If you fire the gun longer than you should, it will damage itself.