Oh, lord, another Savage/Remington thread.
Okay, for hunting (not talking wannabe snipers and competition shooters here) I love my Remington M7 in .308. It's absolutely the handiest little hunting rifle I've ever owned and it's what I reach for anymore when I go hunting. I love the .308 caliber, too. Well, I do use it on hogs and I prefer .30 caliber for that. The .243 is a fine deer caliber and part time varmint gun, but I don't consider it as capable as .308 on big deer and hogs.
I would suggest the Remington M7 as the absolute best choice in a hunting rifle. It's 1 MOA accurate, too, so don't let the soda straw barrel put you off. But, if you can't afford it, the Savage is certainly a capable firearm and will do the job. It's plenty accurate. I'd still get it in .308 between your two choices. I'd steer clear of all those heavy barrel tacticool guns, though, especially in the Michigan woods. I like a light, handy rifle for any sort of hunting, stand hunting or still/spot and stalk type. It's just easier to hunt with in a real world than a long, heavy rifle. A heavy barrel gun might be more accurate after the tenth round (that's why they have heavy barrels), but for hunting, the first shot is what counts. My M7 will hold a 1" 100 yard group with three shots, though, and the fourth and fifth ain't that far off. It'll put five into barely over an inch. I've never tried ten without letting the barrel cool, but why would I care? Hunting ain't about firepower. Barrel weight is simply a liability on a deer rifle IMHO.
You might also wanna look at Ruger and (okay, probably out of your price range) a little Browning short action A bolt. They make guns that rival the M7 for compactness and light weight. I own both a Savage 110 and two Remingtons and the Remington is a more refined rifle, smoother, tighter bolt through, easier on the eyes to look at. But, the Savage works and does it at a better price point. Up to you, really.
At worst, best 2 out of 3 should do it 
