For me, the shortest practical length for a 5.56 AR is 11.5" with a carbine length gas system. I've made a 10.5 run without doing anything exotic, but after shooting both, I find the 11.5" has less drop at 300 yards and enough more velocity to make the extra inch worth it.
Many with combat experience prefer the 12.5" over the 11.5" because they say it gives them better terminal ballistics with military rounds, more reliability and is handier than a 14.5" barrel. I haven't had any reliability problems with an 11.5" barrel and I shoot it a lot suppressed.
If you're looking for the easy button for a good shooting shorty, start with a Colt 11.5" barrel. Or, see what Black River Tactical is offering in that length. Both barrels have the right size gas ports. Use an H2 or A5H2 buffer for softer, smoother felt recoil.
PS- If you don't use a suppressor on your shorty, get an inline compensator. I have personal experience with the BRT Covert Comp. It's lightweight, small, affordable and it works.