With ar15 barrel lengths i recommend a 18 inch barrel. the 18 inch barrel doesn't affect velocity enough to matter. In terms of accuracy i can't tell the difference of a quality 18" and 20" barrel at 1000 yards with .223. Yes that's 1000 yards that i said
Stay away from 24" barrels you will loose velocity with most common loads.
If i were you i would stay away from the 14.5" barrel because you might want to change out the flash suppressor/brake someday. You may also just want to run it without any muzzle device installed. And you loose a good amount of velocity with a 14.5 inch barrel compared to a 16" barrel. But, a 14.5 inch barrel will serve you fine out to around 500 -700 yards.
For most purposes any barrel length will work fine. In my experience from buds it's pretty fast.