For a varmit rifle, I'd take the 22-250. The 25-06 works great but I see it more as a hunting cartridge. You could make whatever you want into a varmit rifle, I used a 338 win mag years ago. It was a hoot but a day with it sored ya up some. As you know I use a 243 now and I like it.
.22-250 or the .25-06. opinions on which is better? Would be for an all around varmit rifle.
Of the 2 you mentioned the .22/250 would be best - the key words are "all around". The .25/06 is a great cross over cartridge when deer are on the menu. Ditto on what ChesterGolf said about the .243, one my all time favorites.
Bring them in on a string. I love this term, if you want to be successful on calling in Elk, try not to just sound like the other caller. We all laugh at each other when we are practicing Elk calling at home or while camping. When I first started calling in Elk, I had no idea what i was doing and it's funny how many I could call in. The biggest Bull that I have called in to date was actually my first. I was making cow calls and screwing it up big time. But it's obvious I didn't screw up...