I've only owned 2, .240 and .257, both on 700 actions. Neither did as well as I hoped.
I would try the .240 again. I like big 6mms. I had a 6 Rem AI for a while which had some issues but when it was having a good day, it was fun, and I had a slow twist 6x.284 that was about as much fun as it's possible to have blowing up small fuzzies.
The other one that calls to me at times is the .224. Set up with a faster twist and configured for hunting, I think it would be a hell of a cartridge. Unless I had a pile of brass, though, I wouldn't go down that path.
