If you want more answers and/or more reading to do, there is an AR pistol section under the AR-15 tab with lots of discussion on shorter barrels/uppers and also an SBR section under the Armory tab with even more discussions. For 5.56, a lot of people like to tag along with the BCM decision to stick to 11.5" as the shortest barrels they use. Pretty much every time someone asks about that write up gets linked.
For me I got both. Started with 7.5inch as when I think SBR, I wanted something that was actually shorter than my 16inch upper and substantially enough to make it worth going through the SBR experience. I then wanted something a little longer along the 11.5inch range and ended up going with a 12inch PSA upper simply because the price for that complete upper during one of their sales couldn't be beat. Unfortunately I haven't had time/energy to get out and truly site them both in and do some testing at 100yards. Really wanting to get a SBR AR setup in 7.62x39, but need to get the two 5.56's 100% before that. The E-file/paper file issue has one of my lowers on hold for now.
EDIT - as mentioned in the post above, check around with the manufacturers of whatever suppressors you are interested in as well since some won't warranty on shorter barrels.