Deerhunt, welcome to the TFL. You're 13 you have plenty of time to figure out what you like. However, if I could have learned one thing at your age about cartridges it would have been this. Bullets matter more than anything else, use good bullets and put them where they belong and you'll be very successful.
As many others have said the .243 is more practical for you than any of the others you mentioned. Pretty much you have picked three identical cartridges, in the real world they all work best on the same types of game. You'll also never see any difference in performance between the three on game animals, only on paper.
I have no experience with the .243 on bear, nor any of the other cartridges mentioned. However, I do have a little bear hunting experience. I can tell you black bears aren't any harder to kill than your average deer. Killing anything has more to do with bullet placement than changing diameter and case size.
Is the .243 you currently have the only rifle you have access to? I'd try shooting other rifles if you can, to see what you might possibly like. The two cartridges you mentioned other than .243 will be tough to find in a pump action Remington as well with probably the 6mm being more common than the .257 Roberts.
Good luck!