RE: the largest caliber for predator hunting
If you want a cartridge with more knockdown power then your .243Win and still be able to take coyote with not too much pelt damage, get one of the 7mm cartridges. You can get fmj bullets for 7mm, which will not create a large exit wound. You can also have confidence in being able to take elk or moose with 7mm. If you do not want a magnum cartridge, go with the 7mmMauser (7x57mm), which is an excellent round, both in accuracy potential and kill power. In a 7mmMag, I like the 7mmWSM. I have compared that short mag to the 7mmRemMag and ballistically, they are very close. the short mag appears to be able to do whatever the long mag can do. With either magnum you will get the knock down power of a 30-06 in the 160gr bullet weight range AND have a rifle that will shoot flatter then a 30-06.