Try .222 with proper projectiles for whitetails. If you are young, that's 'the original .223'. 7.62x39 is a quieter than .30-'06 option too, and super cheap.
The most moose, the world over (a decade ago?), go down to six-five Swede (6.5x55 Mauser), which isn't TOO bad in the house. Nosler Partition 140gr is completely unbelievable. Dandy, though a bit messy, for whitetail too.
The '06 is not that bad after you get used to it, even loaded for bear (literally). In a few years you can turn the new hearing aid off and not bother with hearing protection. It knocked dishes off the shelf when I was young and not as smart as I am now. Mom kicked my butt, but the load completely detached the opposite front leg from a black bear, so it was worth it to me.
My ol' man still tests loads from sand bags on the kitchen table.
We can't speak to each other without yelling.
Must be because he's old now? Maybe Mom's voice is going?
Anyway, neither of us can tell what Mom is saying when we are all at the kitchen table together, so we smile, nod, signal "Fingers in Ears", and keep shooting.
What? Sorry, did you say something?
G-