Take a hard look at the 22WMR (Winchester Magnum Rimfire). There are a number of rifles out there available in this caliber, including my favorite, the older Savage 24 combination gun. In my humble opinion, 22 WMR over 20 gauge is close to ideal for a one gun survival situation.
While the 22 Long Rifle is considered a 75 yard cartridge, the 22 WMR extends the useful range to about 125 yards. For the smallest game, use the solid bullet. You can use the older 22 WRF as an intermediate range cartridge in 22 WMR chambers, but the expected point of impact may change.
As noted elsewhere, 22 RF/22 WMR convertible revolvers are available.
The 22 WMR disadvantages include higher price and a louder report. While the 17's starts with a higher velocity, they run out of energy pretty quickly.
By the way, I'm talking about survival hunting. If you are concerned about a defense cartridge, that's a whole new discussion.
"There is nothing so frightening as ignorance in action."
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"There is nothing so frightening as ignorance in action."