I chose the 308 for hunting deer and elk size game. I use the factory rubber grips and so far, 150 grain Nosler BT bullets. The accuracy and ballistics are great. Sighted at 100 yards, I can hold dead on at 200 yards! Our range is not long enough too shot further so I don't know when the bullets will start to drop. Now for the recoil, I saw a listing on here that said the 308 was not considered a heavy recoil handgun. I am not so sure I agree with that. Shooting off the bench, I seem to get all the recoil I care for. When I am hunting or just blasting away at the gravel pit, I shoot off a set of shooting sticks and the recoil is not bad at all, in part because I am not sitting and braced solid.
The 308 offers a lot of choices in bullet weights and design. There are some big game bullets available in the 110, 125 and 130 grain weights. I like to go to Midway, look up the bullets and then read the reviews. Often I can glean some information based on someones experience with a bullet I may want to try. Even if you don't handload, there is a lot of ammo available to you for this caliber.
I consider the 308 a fine choice for 200 yard deer hunting. Best of luck, Ken