Cartridges...
You already have a .243 Win... Do You Handload? If You do, would You want to take advantage of having powder and bullets for it already, and can You fireform .243 AI out of the .243 Win. brass???
If I were in Your shoes, already owning a .243, AND if I could afford to obtain all that's needed to Handload for the .260 Rem., I'd go with the .260.
There is NOT much You can achieve with the .243 AI that You can't already do with the Original, other than what, 100-150-200 FPS? IMHO, that Original .243 is already plenty fast.
The only knowledge I can lend on a Rebarrel, is when I rebarreled my .270 Win., I went with a Douglas Air Gauge #4 Contour (26" Heavy Sporter), stainless, no flutes. If I remember right, the Douglas #3 is the medium sporter, which would be plenty heavy for either of Your Cartridge choices, and I also believe it's 24". I'd go with the slightly longer 24" barrel, as opposed to the 22", unless it was going to strictly be a Woods Hunting rifle with occasional range trips.
If it were going to be at the range a bit, and a longer range (more than 100-150 yds) target/varmint/small game/medium game rifle, I'd go 24".
For the 'Smith to order my barrel and get the job started, $300. He squared the action, squared the barrel, threaded, chambered, crowned, "polished" then had it bead blasted. Installed the barrel, mounted my new base, rings and scope (I supplied the scope, base and rings, of course), boxed it up and shipped it to me, for another $300. $600 total.
