I am of the opinion that from a practical perspective, for the new shooter only interested in duty/self-defense use, the AR is a much better platform than the shotgun, as it has an easier set of mechanics, much more adjustability (stocks, handguards, etc.), and would be cheaper and physically easier to shoot in general (the last of which can be a serious consideration if you have family members who may also need to pick up a weapon), so training up on it with live fire would be more viable. I also believe that you are being wildly optimistic about just how much less aiming you will need with a shotgun compared to a rifle in CQB distances.
As for the M4/1014 versus the 1301, it is my understanding that the 1301 is reliable with a wider variety of loads (with the M4 tending to short stroke more easily on lighter loads), is lighter, is cheaper, and has a much larger aftermarket. Again, the M4 is by all accounts a fine shotgun, but the 1301 seems to edge it out in most respects.