Quoted:
Make a pistol AR. You wont have to worry about it being a SBR and pinning your suppressor.
Truly awful advice to anyone in a free state.... scratch that.... any state. Selectfire carbine > SBR Semi > 16" Semi > Actual Handgun > AR Pistol > Rocks
OP: Just SBR the AR and get a suppressor later. The SBR is way more useful since 556 doesn't really get any sort of "quiet". Plus with at least one SBR lower you have short barrel options from 22, 9mm, 300blk, 556, etc. You'll find that sometimes you won't shoot suppressed, or if you order a 30cal can it can go on the AR and 308 guns, so multiple uses are something a fixed can won't allow. Cleaning sucks. And certain rails won't work with a fixed can like that. It's not really worth it for most people.
If you absolutely can only do one stamp or live in a NON-SBR state.... 11.5"-12.5" + pinned AAC Ranger3 with the gas port sized/adjusted for 100% suppressed use.