The 223 is my bet, I must have a half dozen rifles and/or uppers that shoot it, and it occupies a big portion of my shooting these days. For 300yd, you are smack in the middle of the varmint application, and any one of many good, popular rifles are available. FWIW, Sierra claims they use the .223 to do their .224" diameter bullet testing.
Varmint rifles have traditionally used slower twists, like 1:12" and are therefore better suited to bullets in the 40-55gr range. Nowadays, makers are producing longer, heavier barreled 223's with faster twists, and these are better suited to the heavier, longer bullets. I have had good results from 24", 1:9" barrels and 75gr HPBT-Match bullets, out to at least as far as 600yd. Faster twists and heavier bullets are also available, but I put the heavies on notice and stop at 77gr. The .223 is a versatile chambering, but I personally feel that going much over 75gr is an attempt to force the chambering to work outside its best range of capabilities, and prefer a larger bore diameter and chambering (my preference is the .260) for the applications folk try to use the really heavier bullets to achieve.
I have 24" barrels with 1:8" twists and they are very nice for shooting smaller groups. I am about to test out a 16" 1:7" barrel with the heavies. I expect good results but it's a completely untested barrel, and still needs to prove its accuracy potential with any bullet configuration.
Barrel weight is another issue. The long, heavy ones don't carry very well, and the weight (mass) is mainly there to absorb heat from sustained firing, like matches or prairie dog hunts. If sustained fire isn't the plan, lighter barrels can work fine, and can be carried around much easier.
As for the heavies, what goes up must come down, and that is especially true of barrel temps. While they can absorb a lot of heat without losing accuracy, they also take a lot of time to shed that heat back down again.
In some instances, the faster cooling of the lighter barrels can be an interesting capability. Combat rifles don't carry a lot of weight, a fact that does not get lost on some communities.
If I appear to talk pretty exclusively in terms of barrels and projectiles, it's no accident. IMHO, the two are the crucial factors in achieving a gun's goals. The other components of the system are also critical, but not to the same key degree.
I have a sternum which has been opened and reconstructed twice, so recoil is serious to me. As one gets older, physical effects of prior injuries mount up, and I gave up the prone position last year; bench, bipod/rest, and bag for me.
While nitpicky handloading can achieve minor miracles, life is short and it's even shorter when you're in your seventies, like I am. I have eliminated all of the special niceties except weighing individual charges. I put my effort into getting good charge weights developed and produced. Yes, I spend most of my time doing load development; but hey, I like doing load development. Unless the rifle has a major flaw, good load development can usually make it a good shooter.
There are more than enough factory rifles that will meet and usually exceed most shooters' accuracy potential. You can replace stocks, and add good optics, but that's not what I call a build; that's home gunsmithing.
Getting a heavy rifle to shoot well is fairly easy. It's not so easy with a lightweight one. But it's also a lot more versatile and satisfying when you can.
My walk around rifle .223 is a Mossberg MVP Predator .223 with the Bushnell 3-12x40 AR Drop Zone BDC scope that is also on two of my three 16" Uppers. Not a match rifle, but it hits what I want it to hit, and the Federal 62gr MSR Fusion load hits hard as well as accurate in the shorter barrels.
Greg
