The .22LR seems the obvious choice for a small caliber, small animal food procurement. Are there others worth considering?
17 Mach II
17 HMR
204 Ruger
223 Predator & Prey
223 Rem
These are the other smaller calibers the rifle I’m interested in comes in. I assumed I'd get .22LR, but have heard a lot of hype about .17. Any thoughts?

Many calibers come and go but the .22LR lives on; why look elsewhere?
I hear those .17 rounds are awsome but how can you beat the reliabilty and availablity of .22LR?
Also by the time you move up to .223 the weight goes up significantly and it blows apart small game.
Yes .223 has more stopping power but if you shot at someone in defense with a 10/22 with a large mag you can keep them pinned down a bit.
There are certain .22LR guns out there that can shoot .22 short and long. Some revolvers convert to .22 mag; I've always wanted a single shot that converts from .22LR to .22 mag.

A single shot, such as the Thompson-Center Contender in .223, with a .22LR chamber insert has always intrigued me. But my trusty ole'Winchester Model 77 (or a Ruger 10-22) with a couple of bricks of hollowpoint ammo would certainly keep me happy...

I love them bricks.

Can't beat the ruger 10/22 and the hollowpoint bricks.
550rnds will go A LONG LONG time in a survival situation.

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."

First off let me tell that I hunt and I'm going to talk about killing animals with different guns. If you're offended by this don't read this reply. My Ruger 10/22 (.22 LR) has killed ground hogs out to 120 yards. The advantage to the semi-auto is that if you miss you can get faster follow up shots. However, the .17 HMR is a far better round for a small game rifle. It's faster, has flatter trajectory, longer range, and terminal balistics is far superior. My personal best one shot kill on a ground hog is 284 yards with my .17 HMR. I heard of one shot kills out to and including 320 yards. That being said, the .22 LR round is readily available, cheaper, and does a good job of dispatching game within its limits. Whatever rifle you get, the shooter has to do his/her part. Practice and get to know your weapon.

CZ 452 Lux in .22 WMR. Excellent accuracy with factory iron sights.

22 WMR is a great round but the problem is that it is not as cheap or as readily available. The 22LR is probably the most widely available small caliber available anywhere. Then comes price.
A box of 50 rounds of 22 WMR is about $7-$10; a box of 550 rounds of 22LR can be had for around $10. That is a big difference. Even someone on a very tight budget can get a 10/22 for around $200 and 5000 rounds of ammo for another $100.

.22 WMR is almost four times the price of.22LR. The 1000 rnds of 40 gr CCI .22 WMR I recently bought came it at ~$190 ($.19/rnd). A 500 rnd brick of the .22LR I like is about $27.50 ($.055/rnd). Still, .22 WMR gives you about 50 additional yards with an accurate rifle.