A few basics -- the parent 284 case is about the same size as a standard .30/06. It is little wonder that a 6.5/06 Ackley doesn't get much more velocity. I shoot one --or really, a 6.5/270. I shoot it because the longer neck lets me shoot a 140-grain flat base bullet, not generally available, as well as bullets with shorter shanks, like the Berger boat-tails. Another reason is the extra velocity, I can get 3,100+ with a custom 150-grain boat-tail.
What I hope shows in this is that there are good reasons for my, and others, using the 6.5 on the '06 case. If you don't have those reasons, there is no special point to it; there is no magic in the chambering. And it is far from obvious that you would have those reasons. That 140 grain bullet is not generally available. The extra velocity is not always usable. As with all rifles, esp. rifle barrels, you may not be able to get to the next "tuning window." Many, even with the 6.5/06 AI have found they cannot; the faster loads are not as accurate. Perhaps certain barrel types help; such as the Shilen ratchet rifle, or the Broughton 5C. There is some evidence, but no proof.
I make the above statements not to start an argument, but to attempt to show that one man's results may be based on conditions not generally stated, or perhaps not generally replicatable -- a certain bullet, a certain barrel.
I'd say for your first rifle, the only decision you need agonize over is the boltface. All of the cases you mention use the same boltface, as do the smaller 6mms used for longer ranges. I would skip the .260 AI, only because it has no history of winning at 1,000 yards. Notice the "no history" -- I wouldn't say "can't."
It appears the early brass issues have been resolved. The plus with the 6.5/284 is the availability of pretty good cases that don't need much forming work. Case forming rivals watching the grass grow or paint dry. You only do it if you really have to.
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Another thought I'd like to stick in here is that 600 yards and 1,000 yards have more in common with shooting; 600 yards and 100-200-300 yards have more in common with chamberings. 600 yards is not long range. 6-PPCs and .30-BRs have won at 600 yards, even though you can't see your bullet holes. (the shooting part). They are not ideal, but they work. They flat don't work at 1,000. Somewhere around 800-900 yards, "mid" range is over and long range begins.
So -- you can use your 600 yard rifle at 1,000, or your 1,000 yard rifle at 600, but it isn't ideal.
The point of this is to decide which you especially want to compete in, and built for that. If you try to build one rifle for both, it will take some luck to be a winner. Yes, the 6-Dasher does win at 1,000 yards. But go look at a match report. Statistically, the bigger calibers win more matches. You have to be a bit lucky to wind up with one of those barrels that will let a 6mm win consistently at 1K.
It is your first rifle. If you get hooked, it won't be your last. The cost of a particular chambering is the dies and the brass and a barrel -- about $500 in components, but everything save the dies is guaranteed to wear out & need periodic replacement.
So make a choice, remember there is no magical chambering --or anything else -- and enjoy it.
Glad you're shooting with us.