The original post:
"I have never owned/trainee on a handgun but am interested in one for target shooting, very close range varmints and last protection. Is it reasonable to consider one gun for all three purposes?"
If you are going to use a gun for protection, you have to have it with you.
I don't argue with that -- but when a beginner asks about a .22 for protection, we do him a dis-service to suggest that it would be adequate.
While I won't dispute your logic, especially regarding helping a beginner, I feel it should be brought up again that everyone here has different needs and expectations. Back when all I had was a Ruger Mk1, I didn't fret about carrying it because I honestly didn't see the need for myself at the time. At home, sure, with my guard down, it felt nicer having something more potent than a baseball bat, but when I went out, I didn't worry about it because I was young, strong, and able.
Yes, .22LR isn't a ballistic powerhouse, but there are loads out there that can rival the traditional pocket pistol calibers at close range, and since it is a more economical and easier to shoot round than most, one would expect a shooter to attain proficiency sooner than on a heavier caliber.
I'm in with the 'hits count' crowd, and discount the 'PCP/crack/bath salts crazed assailant' scenario some have posited. Chances are, if you're roused by an intruder, he'll probably freak out and flee after the first round hits him. In nature predators don't like their prey fighting back and the two-legged type are no different.
In the dark and in an enclosed space, .22 can sound a lot more intimidating than it really is, and sometimes that's all that is needed.