I maybe wrong here, but in today's world I do not think the cartridge you shoot matters as much as the bullet you shoot out of it, and of course shot placement. People kill elk consistently with a .243 win.
You are just beginning the journey, and it's a fun one. Other things to consider is the rifle you want to use, or action you want to build on. I would start there, find what fits you the best and what makes you feel good holding it. Then look at what options in cartridges you have. If you build you can have whatever you want.
My vote though would be on the .280ai. Super versatile, can find factory ammo, but really shines when you load your own rounds.
Good luck and enjoy, this is always a fun time!