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600+ yards with the right shooter and https://www.budsgunshop.com/catalog/product_info.php/products_id/714017014/TRIJICON+ACOG+3.5X35LED+.308+RED+CHV

308 bolt action was (is?) a sniper rifle. 300 yards easy, if you can. I am too old for that myself. Any good scope will work. some where in the $300.00 range probably. The adage is "half the price of the gun for the scope." Brands are personal preference.

Jared, I would recommend a scope that is factory calibrated for .308 Ballistics and 800yrds is the maximum range for reliable hits all day long if your shooting skills are up to par. I highly recommend the Nikon P-Tac (308) Bullet Drop Reticle : https://www.budsgunshop.com/catalog/product_info.php/cPath/26_99/products_id/712016093/NIK+P-TAC+4-12X40+308+MATTE+BDC+800

The scout rifle concept was a battle/survival/hunting rifle for medium ranges with a long eye relief scope of low power and backup ghost ring sights. It was pioneered by the Germans in WW2 and was intended for use to 600 yards. You can take the scope mount and ghost ring off and put a conventional scope on it but why buy it in the first place if you do not want to use it as intended? Here's the scope for it. https://www.budsgunshop.com/catalog/product_info.php/products_id/14885/Leupold+FX-II+Scout+2.5x28mm+Matte+Duplex+%2858810%29