I'd start with a 22 rifle - Bolt, lever or single shot. Autos are a bad idea for beginners.
Should I assume that Ruger 10/22 is the best choice, or are there other good options?
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Shaq was expressing his support for the old truism that a single-shot rifle or a manually-operated repeating rifle is "better" for a new shooter to learn with than a self-loading rifle.
So your suggestion then of the most common self-loading .22 rifle in the country is a little funny!
IF you're asking what you seemed to be asking --
"One of the local shooting ranges offers a kid class with the semi-auto pistols (22LR of course). The other one offers 2 rifle classes. Which one should I sign her up for?" -- then the answer is she'll use whatever rifle or pistol is provided by the instructor and/or range.
If you're asking instead what kind of rifle you should buy for her to use, that's going to be a hotly argued question.
First off, do you want a semi-auto like a Ruger 10/22? No reason you have to get a semi-auto, unless you think that's what she's really going to prefer.
Personally, I like the Savage micros like the Cub-T or the newer Rascal. They've got fantastic triggers and are actually CHILD-SIZED which is important. Most .22 rifles, like the 10/22 or all of its competitors, are built for adults to be easily able to shoot them.
That's not so good for kids. Putting a kid onto a rifle that's actually built to be comfortable for an adult does nothing to promote safety, good technique, or success and enjoyment of shooting.
The little rifles designed exactly for training kids (like the Savage Rascal, Henry Micro-Bolt, and a few others*) are QUITE small and have short lengths of pull which let the kid properly mount the rifle and be comfortable in a solid shooting position, instead of "crawling" the stock and trying to stretch to use a gun that you'd be more comfortable shooting. Plus they're extremely light. Your daughter may be big for a 10 year old, but she's still small statured and not very strong compared to any adult. Give her the benefit of a gun actually made for her to shoot well.
* -- but NOT the "Cricket" rifles, they're poor quality