Best compromise between accuracy and weight is going to be a 16" carbine type profile. There are some amazingly accurate 16 inch M4 profile barrels out there at reasonable prices. I have a true 1 MOA 16" CMMG M4LE (melonite) barrel. I was stunned at how well it shoots. But, pencil barrels are really catching on and there is no reason they can't be accurate, too. It will depend on the manufacturer and attention given in the manufacturing process.
I have a sporter profile barrel on a varmint bolt action rifle that is no bigger in diameter than pencil profile AR barrels and it will shoot 1/2 MOA. But, it is a pretty expensive custom barrel from a precision barrel maker (Douglas). So, it can be done. The issue becomes degradation in accuracy when the barrel gets hot, and smaller diameter barrels heat up faster. If you're not shooting enough to get the barrel hot, it may not matter, if the quality is there. Regardless of barrel contour, a free float hand guard on an AR will let you eliminate any effect the hand guard will have on accuracy, and regular hand guards do have an effect.
A free float hand gard will help any barrel profile perform better.