RE: good overall gun for yotes, deer and varmints?
I would say the .223, 22-250, .243 and the 25-06 would be decent picks if you use the correct bullet for the job. My pick would be the .243 as well. I wouldn't try and pick a bullet to do it all though. I would find a varmint bullet that was really accurate out my gun, then find a bullet designed for big game that shot well. You are not going to need the precision on deer that you would on a woodchuck at 2 or 3 hundred yards.
The .223 and .22-250 would work, and the .223 has the advantage of cheaper ammo. However both are tad light for deer in my opinion. They would work, no doubt in my mind. However they will limit you to range and shot placement.
The 25-06 would work well, but a bit larger than what you really need for your circumstances in my opinion. Now if your main goal was deer with some varmint and coyote mixed in I would say it would be a great choice. The 25-06 shoots about 200 fps faster in most cases than the .243 with the same weight bullets. And it gives you the option of a slightly heavier bullet choice. However the .243 gives you some lighter bullet options than the 25-06 will. The 25-06 is a long action, all the others listed are short actions, it also has slightly more recoil as well from what I understand.
Hornady has a 58 grn bullet with a muzzle velocity of near 3800 fps for the .243. I'm thinking of trying them in my savage 16, my gun shop said they have heard good things about them from customers.
My opinions anyway
Paul