Both are excellent choices, you can't go wrong with either that's for sure.
If you only plan to shoot varmints and such the 22-250 is plenty. If you think you will ever want this rifle to maybe be your varmint/deer gun the .243 would be more versatile.
As for Remmy or Savage, that would be a hard choice for me. I love just about anything on a Rem 700 BUT I'm pretty sure Savage makes a 22-250 with a 1-9tw and that would let you take more advantage of the horsepower with heavier bullets.
As much as it pains me to say this, mostly becasue I think the Savage actions are butt freaking ugly, I would have a VERY difficult time NOT picking the Savage if I were looking for a factory off the shelf gun. Just about all the factory Savages I've been around shoot **** well. That's not to say the Rem 700 factory guns don't but if I were going to take my chances with a factory rifle that I knew I was going to keep "stock", I would probably pick the Savage. Now, if you ever think you will rebarrel or modify the rifle you are looking at getting, a Rem 700 would be my first choice.