GI wannabees
There are two basic kinds of gun buyers, those who are most concerned with performance, and those more concerned with appearance. There is, of course quite a bit of overlap, but these are the general categories.
The M16 has a 20" barrel. This was done for two reasons, one, a handly length, and two, to get the required minimum ballistics from the 5.56mm round. The 5.56mm was chosen over the .222 Remington, because the .222 just couldn't quite deliver the velocity at long range that the military said they had to have. My, how things change. Today the 5.56mm is loaded with a heavier bullet at a lower velocity, AND the military has gone to a shorter (16" barrel) standard for the M4 carbine. They gave up the velocity that they said they had to have, to get a handier package.
A bolt gun in .223 is a varmint gun. Lots of fun, and good for pests and target shooting. A short barrel get you nothing except a handier package for houseclearing and mounting and dismounting in vehicles, and somehow, I don't see a lot of that being done with scoped bolt action rifles.
You want a GI lookalike gun, fine, get one. Get a short carbine or a 20" AR and enjoy it. If you want a bolt gun, 22" is more or less standard length, and varminters can be had with 24" and 26" barrels. Barrel countour has more to do with the weight than the length, and may have an effect on accuracy, but each rifle is an individual, and one cannot in truth say that config A will always be more accurate than config B.
Decide how the rifle is to be mostly used, carried a lot and shot a little, or carried a little and shot a lot. And then decide what is most important to you, sustained accuracy (firing a lot) or hunting accuracy (firing 1-3 shots), and balance that aginst the weight of the rifles, and your shooting style. Heavy barrels tend to stay more accurate as they heat up, compared to sporter weight barrels, so if you plan to fire long strings without cool down between rounds, a heavy barrel might be better. But, packing a heavy barrel varmint rifle up hill and over dale is a pain.
A sporter weight barrel can be as accurate as anything for a few shots, but generally (again, there are exceptions) as they heat up, groups tend to open up. But if packing a rifle around alot while hunting is important, you can do a lot worse than a good sporter wt, barrel.
Short(er) barrel rifles are handier in the thick brush, and at short range the loss of velocity is not an issue. But that kind of hunting is not generally done with a .223, so I would say a longer barrel (to get the most velocity) would be your best bet.