Another vote for the 10/22. But not just any old run of the mill 10/22. I like nice looking rifles and while the 10/22 isn't ugly, it is kind of plain. I had never wanted one until I saw the "Wally World Special." The longer barrel, and checkered birch stock with a rubber butt pad on a "rifle" stock (as opposed to the curved carbine stock on the standard 10/22) looks like a different gun.
Then I found the DSP (Delux Sporter) 10/22. Basically the same thing but in blued steel with a walnut stock.
They cost a little more than a standard 10/22, and I doubt they shoot any better, but they sure look better. They're both reliable and accurate enough for most people right out of the box.
I've got a Remington 597 also, but haven't shot it enough to offer an opinion on it really, but so far, so good.