It used to be that my recommendation would be a used Ruger 77, Winchester Model 70 or similar -- or possibly a new Tikka. The problem is, what used to be common, quality guns that could be had fairly inexpensively have started to become old classics commanding premium prices -- or else new versions of the same coming with eye watering price tags from the factory. These days, for a guy just starting out, I'd look quite seriously at something like a Ruger American. They tend to be quite accurate, have a nearly indestructible stock, and come with a shockingly good trigger.
Get one in .308 Win and you can shoot everything up to and including moose, and ammo is easy to find. But cheap to shoot? Is anything cheap to shoot anymore?!?
If I was in your boat, I would actually consider getting two of those rifles -- one in .308 Win and the other in .223 Rem. Put identical scopes on them, and shoot both -- but try to actually burn out the barrel on the .223 by shooting as much as you afford from every field position you can imagine out to around 300 - 400 yards. Trajectories will be similar -- close enough that practice with one counts as practice with both. And .223 ammo will indeed be a whole lot cheaper to shoot. The two rifle thing may seem costly, but the ammo savings by shooting a lot of the smaller round will quickly pay you back. And all that practice will pay off in spades when you're out hunting.
