Jeff, your "guesses" are pretty accurate and George's advice is good.
I might add that an "optical" sight doesn't necessarily make youmore accurate than iron sights would allow you to be, but they can often make it easier and therefore faster for you to get on target. The tube tends to focus your vision, even if it doesn't magnify the picture, and it is a heck of a lot easier to throw a red dot over an animal than it is to line up a proper iron sight picture.
As for .22s and magnification.. believe it or not, the two of my three most powerful scopes are mounted on 10/22s. I use a 32x and a 24x on competition .22s that never fire at further than 90 yards. I have another 24x scope that is mounted on a .50 BMG.
The scopes maginification should depend upon the use, not so much the weapon you are mounting it on. I like a fixed 4 power or a varible 3-9x for most Eastern hunting rifle applications, but I usually use iron sights on shotgun and muzzle loader becuase of the reduced effective ranges.. even though the actual ranges I have used all three weapons at has been about the same (50-125 yards, typically). This year I am probably going to put a fixed 4x scope or something similar on my muzzle loader.
Getting back to your 10/22 question, the best I can tell you for competition is to get the same type of scope that the people winning that type of competition are using.
For plinking, you'd probably be well suited with a lightwieght 3-9x, I would recommend "see-thru" mounts, so you can use the iron sights in low light, rain, etc....
For Varmint hunting, you would likely be well served by the type of scopes I use on my 10/22s.. maximum magnification.
Be careful abou the quality of the optics when you start getting into the higher magnifications. Once youget over 12x the type of lenses can really make a big diference. I have been very happy with Redfield's high power scopes inthe past, they were probably the best for the money, but I will be ugrading to Swarovski this year. Swarovski won't make a scope more powerful than 24x, primarily because they feel that there clarity would be less than perfect at that level of magification and they pride themselves on trying to be perfect.
I looked through a US Optics protoype 40x at SHOT and almost fell over. It was amazingly clear. You could even make out small differences in color and read small print clearly at over 100 yards. Like Big Marine Binoculars or something. They also said it would cost over $3500, so it'll be awhile before even want one of those!