I'm amused with the way this thread has drifted. It originated with the .17 HMR, and now we're recommending 6.5 Swedes and .243s. I suppose that .270s and the .30s will be next...
Kirby, if you're concerned about report and recoil, look into .22 Hornets. They're far quieter than any of the other centerfire varmint rifles. With the 45 grain bullet, you ought to have no problem with a beaver. They're quite accurate, and moderately priced. Savage offers a combo gun in the Hornet and a shotgun barrel which would be great for a trapper, and NEF makes a nifty Handi Rifle in .22 Hornet for cheap, and can utilize multiple barrels for inexpensive caliber variation. Accuracy can be quite good. I also like that you can put 10 .22 Hornet cartridges into a 35 mm film canister; they're quite handy.