The bolt face is one issue, so any of your shell is fine, but the taper of the case is another factor, so I would not try a 06 case with a 22-250.

Even the 308 can be a bit of a problem when using a 98 Mauser and to get the feed angle of the 25-06/ 270/ 280 30-06 or 338-06 to work with the 243, 260 7-08 and 308 may be a pain.

So if I were you I would probably go with a 270 and a 6MM Remington.

That combination will work well and be trouble free.