RE: best deer and coyote rifle
I've been using the 243 for my main coyote gun for a number of years now. I load Hornady 75gr HPs around 3200fps (under max load), and out of 100+ coyotes I have harvested with that load, I have only had a few that the pelts were wrecked. This was my fault because I put the bullet in the shoulder blade (something you never want to do on a fur-bearer if you want to keep the fur).
I've always shot a # of coyotes with 95gr Combined Technology BTs loaded at 3200fps, and didn't wreck the furs. So in my opinion, the 243 is a great fur shooting gun.
I've seen a few 25-06 kills on 'yotes, and none of them were salvagable. But I'm sure with the proper bullets they would be.