I have a friend that picked up a Marlin 795, and for the money it's awesome. Seriously, it's almost half the cost of the Ruger 10/22 and just as good.
That said, my choice would be Ruger 10/22 "all weather". It's the model with the plastic stock and "stainless steel" barrel and receiver. I've been shooting out in the rain, snow, and forgotten to clean it...treat it like a hot girlfriend that cheated on you, and it's had near flawless operation (I did have the extractor wear out on it prematurely which cost me $10 to fix with a better aftermarket part).
The 10/22 is a fun rifle because it's accurate out of the box, and you can build it up, or just leave it be and it's still fun. Seriously, you could spend $1500 (on a .22!) and really make a laser accurate, cheap to shoot rifle...or you could just pick a model with a pretty stock and use it till you die and leave it to your kids in your will.
Oh, and if you want a 10/22 that's a little more comfortable, and you don't plan on modding it, consider any of the 10/22 that come with the Hogue Overmold stock. It's a stock with a plastic core (so the receiver has a solid base to mount to) that's completely "overmolded" with a tough rubber. It's very comfortable, mid-weight, and you again don't have to worry about weather effecting the stock. It's more expensive than the base model 10/22 or the "all weather", but for a rifle your not going to modify, it's very good.
Edit to add: It looks like the Ruger All Weather are getting harder to come by. You might hit up a Walmart that carries rifles, they were the main seller of the 10/22 All Weather. But here is one on Gun Broker