Between the two calibers you listed, it depends if you buy factory or are a reloader. Factory 223 is cheaper than 22-250, but if you already load the 22-250 is the better round.
Bolt action is the way to go, but watch the barrel twist rates. I have one 22-250 in a 1 in 12 twist that will not stabilize any projectile larger than 40 grain. So if you want to lob the larger wind bucking pills get a gun with a tighter twist.
If you are calling, not spending a afternoon at a p dog town, most sporter weight barrels are fine. The heavier barrel will kill them really dead, the sporter still dead. Dead is dead.
Might want to consider another round or two, definitely 243 and maybe a 25. My reasoning is if you call at the same time Deer season is open. Target of opportunity, but the 25 has few true varmit projectiles for reloaders. I use a heavy barreled 25-06, and use a stout projectile, trying to not hit major bones on predators. One projectile/load for both purposes. A good penetrator for deer, and no grapefruit sized exit wound. Small hole in small hole out. Less sewing.
I am not a big fan of Savage. The problem here is if you insist on a detachable mag. Many more with floorplates than mags. Since you are a member, hopefully use the equipment exchange, keep a eye out there. Round count in predator calibers is far less a issue than in a large magnums like the Rum's. ( maybe excluding the 220 Swift and 223 WSSM ) I have never had a problem with a used firearm, especially if you can examine it first for condition and send a light down the tunnel.
Bryan