As far as 22LR......AmmoFast.com has a reliable supply...but the shipping is what kills.......locally, WM, nadaYou won't regret purchasing a 10/22. Ruger stands behind their products better than any company I know, and the 10/22 is an extremely reliable and dependable rifle. Your bigger dilemma will be finding some ammunition for it.
I just suggested to my older daughter, the Ruger American .22 for my grand daughter ( prefer bolt over semi-auto ).I can't think of a better all around first rifle. They are endlessly upgradable and customizable. Very reliable and easy to work on. Inexpensive as are most of the parts (except custom triggers which I wouldn't suggest until you've got alot of lead downrange and you decide to build a precision tack driver).
For safety a semi-auto isn't the best way to learn to shoot and concentration is needed to remember there is another round in the chamberPros; Compact, easy to use, accurate. Fun for new shooters as you can easily hit what you're aiming at. Ammo is cheap. Original cost of 10-22 is relatively low.
Cons; Semi-auto,stock may be too short. For safety a semi-auto isn't the best way to learn to shoot and concentration is needed to remember there is another round in the chamber. Many use the 10-22 as a single shot until safe gun handling is learned. On my 10-22 carbine the stock is way too short and I have to scrunch up to see the sights. Not a big deal with smaller folks.