I would take a long hard look at what is available on the ammo shelf. Unless of course you don't care when you might shoot your new rifle.
I would certainly not consider .223, or .308 for that matter. Plenty of rounds that can match them and not be over priced or unavailable.
The .243 has plenty to offer in the whitetail and under category. The .270 for moose and under category. The more unique a round is a person would do well to stock pile a hundred rounds of hunting fodder. Then you won't be at the whims of the factory, to decide to tool up for .257 Roberts, or keep on keeping on with .308.
This is my personal strategy, I have enough ammo sat aside to last about two hunting careers for each hunting rifle. I'll never be lucky enough to fire a hundred rounds at elk with the 300mag, including practice, same for the .325mag, and the 45-70. I'll buy ammo to shoot for fun but the inventory stays the same, a hundred on the shelf and 20 in the range bag for example.
A final thought, save your brass. Some day pick up a couple boxes of bullets and an equal number of primers for that brass. If what you own is quite unique pick up a die set one day. You'll run across someone who will be willing to show you the ropes one day. That afternoon you'll go home with "nearly free" ammo.