Most factory .308s come with a 22" barrel, which works well with it's moderate velocity. Adding a couple inches to 24 may give you 50 FPS more, but you might even find that kind of variation from identical rifles' slight differences. Most .308s come today with 1/10" twist rate, which works well with most bullet weights from 150-180gr. Your particular rifle may favor one weight (or brand) over another, but you'll only find that out after shooting a few different weights and types.
I'd also agree that the .308 is a very fine choice for your needs and is known to be a cartridge known for good accuracy. The other plus with a .308 is that it comes in a LOT of different rifles and models, maybe more than any other caliber. This gives you a huge range of types, models and most importantly prices for you to look at when choosing your rifle. If you're not worried about minimum weight, perhaps some heavy barreled models might even look good for your wishes. Generally speaking a heavier barrel will give you better accuracy, being stiffer and able to handle heat more effectively.
Good luck with whatever you choose!