I did some testing on effectivity of companions with various ranged weapons. Apply pretty much on settler AI as well. It was done purely by observation so don't take it as a strict truth. Anyway, here is what I found:

AI does seem to be more effective with weapons which have good hip fire accuracy (indicated by size of aiming cross when holding weapon and not aiming). Whether that means that AI actually use hip fire, aimed fire, both or if it use it's own mode I don't know. There does not seems to be much difference as far as size of recoil is considered. AI have bad accuracy at long distance, no matter the precision and range of weapon. Sacrificing other attributes for range is a bad choice in choosing companion weapon. You can obtain the best performance with weapons with good rate of fire, medium range, good hip fire accuracy and as high damage per shot as possible. Automatic weapons are devastating at close range in the hands of AI but they does not seem to outperform their semi-auto equivalents at mid range. AI is really wasteful with ammo when using automatic weapons and produces lot of misses at mid range. Your active companion will burn through his or her ammo really fast. Of course that's not an issue with dismissed companions and settlers since they don't use up ammo.

I did not test all weapons, but among those tested good choices are: Laser Rifle or Pistol, Combat Rifle, Assault Rifle, 10mm Pistol, Minigun.

Weapons with high damage but slow rate of fire did not perform well so you should avoid them: 45. Pistol, Hunting Rifle, Laser Musket.

Combat shotgun was total disappointment. In hands of AI it is effective only at point blank range.

I also tested Pipe Rifle in armor piercing auto modification and powerful semiauto modification. Long Fined barrel did not work well but automatic version with short light barrel and semiauto with long light barrel worked reasonably well for this low end weapon. Not bad choice if you want to get rid of large .38 ammo stockpile, but don't expect miracles.

I tried Gama Gun and AI did not perform bad with it. Problem of course is, that some enemies are immune to it.

As far as modifications are concerned, light barrels, especially short ones seems to be way to go. Recoil reducing modifications does not seems to have much if any effect and same seems to be valid for various scopes and sights. You should generally avoid modifications which reduce hip fire accuracy. Damage or fire rate increasing mods are always welcome. Bayonets can be fairly useful, since AI does perform bashing attacks at close range. Clip size and reloading speed mods are welcome.