I think if you're going to buy a long gun, get something in a long gun chambering.
The benefit of a long gun over a handgun is the larger caliber, why negate that with a pistol caliber carbine (PCC)?
According to THESE GUYS, the difference between 5" barrel and an 18" barrel for some 9mm ammo is less than 200FPS in lots of cases results will vary with ammo type of course), the velocity of a rifle round in the same length barrel is almost 2-3X that of the 9mm.
As for the .223/5.56 vs. the .308/7.62X51...that battle has been going round for decades. As for the deer hunting thing, many states limit the caliber to .30cal and above, that omits the .270 which is a fine round and in most some cases these laws predate the mass civilian use of the .223.
I prefer the handling characteristics of an AR in 5.56/.223 or 6.8 to those of most .308 semi-auto rifles and they are cheaper to shoot.