Not another what rifle thread

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So another wet day and the brain doesnt go into stop thinking mode. Got a barrel in the swap section. Had a rem600 sitting around in 243 tried a few things with it but Im pretty sure the barrel is past its use by date. What are the cartridges that can be used in this action using existing bolt face. One option could be a fast twist 243. Me liking stuff thats not fashionable and a little bit odd ball was also thinking a fast twist 22 250 or a 257r do these 2 go in a short action or possibly a 260 but I already have enough 6.5s? Any other ideas?