If you are sticking to the AR 15 platform then I also suggest the 6.8, as you are not a reloader, ammo availablilty is better than 6.5, I am pretty sure. As mentioned before you can always get a 223 upper for it later.
If you want to go with a 243 or 308 then you will have to move up to the AR 10 platform (or should I say 308 platform), if you go with this platform it will be heavier because the receiver and mags are larger to accommodate the longer overall length of the 308 (or variants) cartridge. With this platform some of your common cartridges are 308, 243, and 7mm-08.
With both platforms if you ever decide to start reloading then your options go up exponentially.
As for your question about the Remington R-15 (ar 15 platform) I believe the only chamberings available are 223 and 30 AR. And the R-25 (AR 10 platform) I believe the chamberings are 243, 7mm-08, and 308.
Hope this helps