In my opinion you are overcomplicating skills. UFO is no RPG. Why would a rookie soldier be unable to use burst or full auto of his assault gun, if he wishes so? If his strenght is too low to handle the recoil or accuracy too low, then he will not achieve the desired results. Simple as that.
One thing, which skills could improve, would be reaction speed or in game terms - probability of reaction shots.
If TU costs for firing will become proportional to the speed (i.e. in %) rather than flat TU costs, then weapon skill could also reduce firing costs, say by 1 TU for 25 points in skill.