I found a Weatherby Vanguard, (Made for Weatherby by Howa, Japan) synthetic stock, Leupold 3 - 9x VX III on it, in 85% condition (easily) in a pawn shop for $350 out the door. Locally there's a decent gun shop and the regulars "change rifles" like most people change socks. Lots of stuff on the rack in the $350 range . . .
Most used guns are in the shop because someone got "tired" of it, or needed some $$$. Never have I bought a used gun that wasn't completely straight. And the shop will back it up if it's not straight.
30-06 is pretty popular. Out in the boonies you can find 30-06 ammo anywhere -- Bubba will have a box in the truck, or a few rounds behind the sofa cushions.
30-06 bullets are .308" dia. and available from 65 gr. to about 225 gr. As noted elsewhere, the 30-06 will manage any game in No. America -- with the possible exception of prairie dogs at 300 yds. But then if loaded right, the 30-06 will have the dogs put on notice too.
But I'd suggest you start looking in the shops, get familiar with calibers, and see what's available used. Learn to know a decent scope from a cheapo . . . (Hard to go wrong with Leupold, and it's a local product here.)
For your applications, you could go 270, 243, 30-30, 44 mag. carbine, 308 Win. 30-06, 6.5 X 55 Swede, 8mm Mauser, and some others.
This might be your "first rifle" but there's every chance it wont be your last.
Shop around in the used section until you have a feel for what's available, and eventually there's gonna be one that tells you to take her home . . . Just like goin' to the dance on Friday night.