I have four different .223s and various bigger bangers incl 6x47L. I once owned a .22-250 but the extra bang just wasn't justified. The 6mms walk all over them at long range.
If I was starting out again, I'd get a .204 based on my experience with a mate's Tikka Varmint. Stonking accurate and you easily see hits through the scope. He knocked over three rabbits recently in five successive shots. Closest was 375yds and the two misses were so close, I don't know how the rabbits escaped. We were laughing away, very satisfying. Would have been five dead foxes for sure.