Simple answer - Generally speaking, the shortest length you can use for your application.
Why? We are strong believers in maneuverable weapons. The shorter the barrel, the less weight and momentum on your firearm.
Unfortunately, the non-simple answer is quite complex, as it depends highly on a number of factors including but not limited to:
The Federal Government has set the minimum legal length of a barrel at 16" before it is considered a "short barrel rifle" or SBR. Customers will want to ensure their compliance with the federal and various potentially stricter state laws on the configuration of their barrel.
It should be noted that customers can own barrels shorter than 16" so long as they are equipped on a legal SBR, machine gun, or legally constructed as a "pistol." Please consult with outside legal guidance on the formal definition and construction of a "pistol" under Federal and state laws.
Customers are advised to always ensure their weapons are configured to be compliant with all applicable laws.
Maximum Intended Engagement Distances:
Faxon recommends that one choose a barrel length that will keep the round supersonic and stable across its flight. and above the minimum effective velocity for the bullet's design. For example, a 10.5" 5.56 barrel is "effective" (by terminal performance and bullet-drop) to 150 meters, but one will want a 16" for sufficient velocity out to 500 meters.
Customers are advised to choose the barrel length that will keep the bullet supersonic and stable to their maximum intended engagement distances.
Highly correlated with the engagement distances mentioned above, the caliber will determine the needed barrel length to reach the needed velocity to maintain stability and ballistic effect downrange. For example, both .300 Blackout and .308 Winchester use the same bullets, but .308 Winchester has significantly more energy by nature of the larger case capacity.
Many calibers and/or bullets have minimum needed velocity for their intended terminal performance. 5.56 / .223 Remington is well known for needing velocity for terminal effect with common 55 grain loads. With some loads, like military surplus 55 grain 5.56 can lose its terminal effectiveness while still maintaining supersonic flight and stability. A hunter will want the velocity at his engagement distances, but a competitive shooter can be OK with just stable flight to ring steel - which can be hundreds of meters further than the required terminal velocity.
Suppressors & Muzzle Blast
Typically suppressors are rated by caliber for a minimum barrel length. This rating is set by the pressure of the powder charge versus the length of the bore. The longer the barrel, the less the pressure when the bullet enters the suppressor. Customers will want to ensure their barrel meets the minimum rated length for the suppressor. This rating is set by the suppressor manufacturer.
Further, customers will also want to be astute to the same pressure if using a muzzle device. On extremely short barrels, like 7.5" 5.56 there is significant amounts of unburnt powder at uncorking, meaning loud and large muzzle blast. This could be exacerbated by a muzzle brake. Customer should go no shorter than their personal comfort level and amount of safety equipment including hearing protection.