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The 22-250 and the 243 would be a little light for those in my opinion (More of a varmint round). The 25-06 is on the bottom end of what I would suggest. Everything else you listed is more than capable, in my opinion, of doing what you want if you can stand the recoil. I know a gentleman who swears that my .270 is the devil's own spawn, but has no problem shooting his .308 which is setup identical (Manufacturer, model, stock, scope, ect.) to my .270. My advice is to shoot some bolt guns in the different calibers you are considering and decide which one you like the best. I would suggest you try out the 308 or the 30.06 first. As for the Savage I have to say I have never been disappointed by one, although I have not shot that model.

What are you going hunting with the gun? You say medium game but what do you consider medium game? Dear, hogs, elk?