The easy thing about the 6mm-06 is all you've got to purchase for brass is the 25-06 or .270 win cases. The 270 cases work well.
100 bucks for a sizing die from RCBS. Maybe cheaper elsewhere, I don't know.
You can seat the bullets with a .243 win seater.
I think the 284 brass isn't so easy to come by in most parts. 270 brass nearly grows on trees.
As to the .22 cal option, if you're punching paper or shooting at smallish game, that's worth considering... but again, you'll have a gun that uses an esoteric brass, and if you want to step up to a larger animal you might want a 100 grain bullet, which the 6-06 will push to well over 3000 fps.
I think if there's another cartridge worth considering over the 6-06, it would have to be the 6.5-06. Brass availability is the same, and extremely high BC bullets are available.
But pushing that 87 VMAX toward 3700 fps makes for a great long range dog and varmint rifle, and of course deer have gone down to lesser combinations as well...
Accuracy from a 6-06 is excellent. Sub MOA at 1060 yards last time we tested my cousin's rifle. And that was a 5 shot group... generally he'll shoot 3 shots.
It's just the barrel torching issue that must be considered... as all that power and flat trajectory is gonna cost somewhere.
Dan