First, I'd recommend something bigger than a .22, but I understand that you gotta do what you gotta do.
Usually, a revolver is the best bet for beginners. But, there's a reason or two that they are good for anyone else, too. Primarily reliabilty- a small .22 revolver will usually be more reliable than a small .22 semi-auto. The swinging hammer gives a harder hit to the rim, which can be crucial with getting some ammo to work all the time.
The bad thing is, double-action .22 revolvers are harder to find than .22 autos. There are several decent single-action .22 revolvers, but since your already handicapped with a .22, don't make it harder.
Also, I usually suggest a stainless steel gun for someone who may not be "into" this gun thing. If it lays in the sock drawer for the rest of it's life, it shouldn't be all rusted up the next time it sees the light of day.
The S&W model 63 comes to mind first. It's a J-frame (small frame), six-shot, stainless steel revolver with adjustable sights. I really don't know if it's still being made.
The S&W 617 is nice, but quite a bit bigger, if that makes a difference. If it doesn't, they make at least one variation of the 617 with a ten-shot cylinder.
Ruger makes the SP101 in .22 also. It's like the S&W 63, but a little bigger, and the rear sight is adjustable for windage only.
Beyond that, be careful. There is a lot of junk in the .22 revolver world.
If you are set on an auto, stainless steel may not be an option, except for the Ruger. The Ruger has a great reputation. I've had three, and shot one a LOT. Ruger is either changing it, or adding another variation, so you might want to see that before you decide.
Ditto what was said about the Walther P22. See the Walther section of
www.rimfirecentral.com for some reports. It's neat looking, and feels good. I had one briefly, but traded it for something else I wanted, before shooting it.
The one and only small .22 auto pistol that I can recommend is the Beretta 21A. Neat gun. I bought one when I lived in an area with no carry provision. I suddenly found the need for a really small pistol.
Anyway, the Beretta 21A I have has over 5000 rounds through it. I know this for a fact because I bought a 5000 round case of Remington std velocity ammo, and used it all in that gun. It's had a lot of other shooting too. I used to belong to a club with it's own indoor range, and got off work at 4:30AM at the time. Not much else to do that time of day except shoot.
Although the finish is mostly gone, it still works great.
I don't know if they make it in stainless yet, but they make the .32 version in stainless, so they might now.