The best thing you can do is start handloading as you’ll no longer be stuck with factory options for monos. That said, for an off the shelf rifle, with widely available factory ammo, the 270 is a great choice for shooting monos. The 6.5 PRC works too, but with monos, offers no real advantage over the 270. BC is a thing, and makes a difference, but for 600 yards and in it’s not absolutely critical that you have a suped up, ultra high BC bullet. I shoot steel to 600, in wind, with my 270 and the 129lrx, and can hit the 12” plate with boring consistency. You do want to be mindful of your velocities with monos. That load I’m shooting is 1900fps at 600 yards at 1200’ elevation, and 2100fps at 600 yards at 7500’ elevation. Longest I have killed with this setup was 480 yards on elk and it tipped over dead. Wound channel was not impressive at all, however I put the bullet where it needed to go. I handload, and if I was starting from scratch with the intent to shoot monos I’d probably get a 6 creedmoor. Muzzle breaks are an absolute hard no for me.
Practice, practice, practice. 600 yards is a long ways to be shooting at animals. Nothing wrong with practicing further out and imposing some limits on how far you shoot at animals.