I have/have had, a number of .308 bolt guns, and a number of them were not something Id want to carry around and try to hunt anything that might need quick shooting or quick follow up shots up close.
I did have a Savage Scout, and it was about perfect for that. Light, easy handling and very accurate. Nice big bolt knob, that was easily and quickly worked. It lacked a stripper guide, but I guess nothing is perfect. Scout scope works well for quick, close up shooting, and is OK for longer shots, but I still prefer the irons or a red dot for that.
My favorite for a long time has been my little FR-8. A little heavier than the Scout, but it has good, useable irons, and a straight bolt handle that works fast and easy, and is accurate. It does have a stripper guide.
My .308 autos werent quite as handy and a bit heavier than the carry realistic bolts, but if youre in reasonable shape, they are not at all a hindrance. My overall favorites were my HKs, but (lacking an AR "carbine") my M1 would be my next choice. The M1As were "OK", depending on the era, but they just arent as handy as the M1.
While not a .308, but still .30 caliber, I really like my AK's in 7.62x39. Its like a .308K, and the guns are handier, lighter, faster and easier to shoulder and shoot quickly with, and even with just the irons, will easily fit the 250 yard limit.
For anything serious, Id go with one of the autos, and these days, it would probably one of the AR's, simply due to the versatility of the platform. As much as I like the right kind of bolt, even when stripper fed, they just cant keep up to the autos.