After looking it up in the GECK:
It stats that it affects only weapons with animation types 5 and 6. So it would be safe to assume that one of the types is TwoHandRifle.. However, since there's two, and there's TwoHandRifleEnergy, then I'm inclined to say that those two types are the ones that Commando affects.
Any automatic weapon, it seems, isn't affected by Commando, as weapons like the LMG or Laser RCW belong to the TwoHandAutomatic type and the minigun belongs to the TwoHandHandle type.
EDIT: I could be misreading the requirements though and by animation types 5 and 6, it means something completely different. I'll look into it a bit more.
EDIT #2: It would probably be best just to test this in-game by doing a before and after comparison of % accuracy in VATS on said LMG and Minigun. The only conclusions I can come from by looking at the GECK is that it's either what I mentioned at the beginning of this post or it's TwoHandRifle and TwoHandRifleEnergy sharing the same animation type, and then it's either TwoHandAutomatic or TwoHandHandle.