In my opinion, you positively can't beat a Marlin 1894C for the use you stated. It's light, accurate, tough, and cheap to shoot if you're a handloader.
Like SUSQUASH said, it's a great short range deer rifle, and it's extremely versital from small game hunting to busting predators. I've used one for years on everything from squirrels, and rabbits, to coons, groundhogs, foxes, turkeys, and plenty of deer.
A good 158g SP bullet pushed to around 1700-1800 fps is serious deer medicine up to 100+ yards, and you can achieve this with quite a few powders.
Personally, unless I'm specifically hunting deer, I shoot a mild 357 load in my rifle. For small game like squirrels, or rabbits, your best bet is 38 specials with 125g SP's at around 700-900 fps. You'll get great performance without blowing them up. For an all around plinking/carrying load, a 125g SP loaded to around 1400-1500 fps will take care of anything you'll ever likely shoot out to 100+ yards. I've killed groundhogs past 200 yards with this combo, although that's the extreme limits of it's effective killing ranges on them.
Here's a load that has been very accurate in every rifle, and revolver I've tried it in(there's been a bunch).
125g Remington SP's
CCI 550 primers
7.5g of Unique
This combo will give you roughly 1450-1550 fps, and will reliably thump anything up to coyote sized out to 100 yards. It has very little recoil, is extremely accurate in rifles, and is perfectly safe in any 357 magnum. It'll handle a deer up to 50+ yards with perfect shot placement in the vitals on broadside shots, but I wouldn't push my luck too far on a deer with it. It's quite a bit for squirrels or rabbits, but I've killed a lot of them with it using head shots.
Hope all this helps?