it may be fair to say different people take different approaches and have different views of shooting, gear, capabilities, use cases, etc.
to keep this response reasonably short, i would like to say that if you are truly only going to shoot 10-20" targets at 1000 yards, then your requirements are going to be quite different than people who might want to shoot different ranges, unknown distances, different size targets, both shooting larger targets faster, and shooting smaller more challenging targets. (both of which are more fun) adding time, positions other than prone, and practical applications (2A scenarios) all change the requirements dramatically.
as far as the scope is concerned, I can't tell you how annoying it is for people to say "what scope for x yards?" when distance has almost nothing to do with it. distance does not dictate your choice of knobs, focal planes, magnification range, reticles, glass, parallax adjustment, illumination, durability and water resistance, etc. for example, high power shooters have shot 1000 yards with iron sights for longer than i've been alive. as long as it holds zero, just about any scope will do. and a $3000 scope isn't really going to buy you any points over a $500 scope. you don't need to distinguish the targets beyond seeing a giant number board, etc. that is definitely not the case in the PRS, or practical shooting.
as far as the cartridge is concerned, 22 is a suboptimal choice unless you have other issues. a 6mm would be a much better choice.
hot rodding a 22 may get you on the target at 1000 yards, but it may damage steel at closer ranges, and you'll have more difficulty seeing trace and impacts, both hits on steel which disturbs the paint much less than larger calibers, and misses which kick up a lot less dirt.
6.5CM is a better choice than 260rem.
i can't speak to the rifles you've mentioned other than to say the most important thing will be to find a stock you can comfortably shoot from whatever position your friends normally shoot (bench or prone) and that won't result in fatigue to your neck, etc. the heavier the better.
I’ll also say you should ask yourself how much more fun hitting targets is than missing them. If you expect Hitting that target 1 out of every 4 tries is going to be a lot of fun for you than sure a 308 will be fine.
And also consider how many rounds you shoot per range trip and how many range trips per year. Putting $2 through the barrel every time you pull the trigger adds up faster than you might think. Even if you go to the range once a month you will probably spend twice as much on ammo as on the guns you’ve mentioned just in the first year. Long range is an expensive sport and missing a lot just isn’t that fun. If you’re going to do it, do it right.
