A quality AR in 6.5 Grendel is what I would tell you to build. Just more fun than bolt guns, plenty accurate and with certain bullets it's still supersonic at 1200 yards out of a 20" barrel which not even the 7.62X51 will do.
You mentioned that you had a red dot on your AR and I got the impression you didn't think it would do 1 MOA. Could be the red dot. I could hit 8" steel at 300 with my wearing an Aimpoint with a 4mil dot but I couldn't call the shots until I put a scope on it. It was a "Shoot all around it" proposition until I got the ring from the hit. With a scope I get actually get bored at 300 on a bench. My ARs are nothing special either. One is a bone stock M&P15 M4 clone and the other is an 18" mid weight DPMS barreled franken upper that I use for 3gun. Both will hit 8" steel at 300 every single shot off the bench with run of the mill 55gr FMJ loads. Will they do better with a killer handload at 69 or 77 grains? Danged if I know, I've never seen a need to find out. Going to 500 will probably need a good 69gr SMK handload. Bottom line is put on a decent piece of glass for distance work. Some red dots are okay for about 200 yards but that's really it. The 1x6 tactical scopes out are really good and some are even up to 1X8 now.
Build a nice 6.5, put in a decent trigger and piece of glass, get a bi-pod and you'll be able to hit farther than you'll want to.
Thank you very much for the input. I have an MPX 9mm for my up close and personal weapon. I have an AR (now for sell) that I have no doubt would be more accurate than I can shoot. I was more curious about having something to reach out and really put a thumping on something if need be. I did not think there was one gun that could go out and make the hit and also be okay for a cqb too. I'm extremely limited in my rifle caliber knowledge. I will look into the 6.5.
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