I echo the 30/06 choice. Effective, affordable, available. It's pretty hard to beat when considering those specific criteria. You'll be likely to find whitetail and/or elk ammo in almost any place that sells ammo.

Little mom-n-pop stores that sell food and beer/wine, if they have any ammo at all, will likely have 30/06, 308, 270 win, 30-30, .22 long rifle, and maybe a handfull of shotgun choices.

Plus, it has taken more than a few elk and moose over it's history. There may be better choices when polling thousands of folks, but it still makes sense, especially for you.

Your other rifles aren't exactly rare or eclectic, but still, finding ammo for them isn't as easy as finding 30/06 on the shelf in 150 and 180 gr pills.