For an AR, I would get a 6.8SPC caliber carbine to hunt deer with. But if you load the right bullet into a 223 bore with the correct twist rate, they will work great too.
The 357 is more or less a 100 yard deer rifle. A good option is the right-handed Ruger M77/357, even if you shoot lefty.
I do 100% of my deer hunting with a Marlin lever action 336. I use both the 30-30 and the 35 Rem. Be careful shopping for new Marlins. They are now made by Remington and quite a few bad ones have slipped out the door. I now buy used.