Forget the Arc Thrower against Illuminates.
Just don’t do it. It sucks.
Take anything else. Use your pistol. But Arc Thrower against Illuminates? Big NO!
The Arc Shotgun, however, is pretty much the best weapon against Illuminates and it destroys them like they’re nothing. If you want to feel like an untouchable wrathful GOD against the Illuminates, try the Arc-Shotgun with MD-99 Autoinjector perk and the SH-32 Kinetic Directional Shield (the DLC shield form the Entrenched Pack).
Ok, so I don’t apporach the Arc weapons like I would any other primary weapons; instead I think of the Arc weapons as specialized weapons, as Stratagem/Support weapons that can not be dropped and also do not need to be called in.
So, the Arc Thrower is beasically a Heavy Sniper Rifle with a long charge-up that gives you the ability to dispatch entire patrols from far away (this is most useful against Cyborgs because their patrol units are the most resilient), so it’s best used while defending objectives or teammates.
When traveling the map I would always switch either to my sidearm (preferably the Gunslinger DLC pistol or a secondary weapon such as the Machine Gun or Dum Dum) to deal with patrols.
This also means that I very often bring Ammo when I use the Arc weapons (which runs counter to how everyone else seems to use these weapons), because I know that I can not rely on these weapons in the same way that I would most other weapons.
The Arc Shotgun, on the other hand, is a bit more flexible than the Arc Thrower and I feel I can use this weapon a bit more aggressively. The charge up time is a lot faster and this weapon good for dealing with certain mobs (especially Illuminate Tripods and Bug Warriors).
Both weapons have their own respective quirks, btw. These are specific to each weapon:
The Arc Thrower can jump from target to target, which is how it can reach such high distances (i.e. killing a full patrol all the way on the other side of the screen), the range however, can artificially be extended by SH-20 Bubble Shields.
If you ever find yourself with a fully charged Arc Thrower, an incoming Cyborg patrol, and a teammate wearing a Bubble Shield between you and the patrol, blocking your shot and alerting the patrol, then take the shot.
Your teammates shield will need to recharge, of course. But while the shield is active it can and will serve as a conductor for the Arc Thrower shot.
The Arc Shotgun has a completely different quirk: it can shoot through solid terrain.
Stand against a wall or piece of cover. Charge your shot. Wait for patrol to walk on the other side of whatever solid piece of terrain your standing near. Shoot. Wait for next patrol. Repeat. Remain unseen.
That’S all for now, I guess. If you have specific questions then just go ahead and ask. This is all just from the top of my head, but I’m sure there’s lots more.