What kind of budget do you have for the scope? Is the gun for all around use where a variable would be helpful? Seems like variables dominate the shelves these days.
If I could sort of generalize, 22 scopes seem to span the greatest range of price and quality you'll ever find. You can pick up a very wide range of scopes in the less than $150 range that will make most of us happy, but none will be high quality, but that may not really matter to you (or me). If I'm out deer hunting and spend 3 days waiting for my one shot, I've got a lot invested in that scope and rings being dead on repeatable accurate. On the other hand if I buy an $80.00 Bushnell for my 22 and 9/10 its still dead on, but the odd time I have some adjustments to make and during those adjustments it doesn't seem to alway track smoothly, I can live with that.
If you are going to shoot rabbits and gophers and squirrels and prairie chickens, you are going to want something that can go down to a low range of magnification, like 2-4x. If you are strictly shooting gophers at a distance, or targets at 50 yards or more, you'll appreciate lots of magnification and a sharp image. So I'd say a variable with a top end of at least 9x for that use.
I am very happy with a 4.5-14 x 40 AO scope I put on a 223 rifle and I'm going to put another on my CZ 452 bolt action rifle. The scope is made by a company called Meuller. The cost around $190.00 and have a really nice clear image. I have a 3-9x40 Bushnell AO (adjustable objective ) scope on it now, and I don't like the image quality. I guess I'm a bit spoiled.
The adjustable objective is nice because rimfires are often shot at close range and expectations of accuracy are very high, and adjustable objective allow you to reduce the error causes by parallax, that's moving your eye causing the apparent point of aim to change. Scopes for centrefire rifles usually are not AO, and are set for distances beyond that which rimfires will be used, so they may not be suitable for shooting a 22 at close distance.
There are guys on here who like their $100 tasco varmints that are 6-24 magnification, but they do say the image is blurry at the top end of the zoom. I've never used one, so I can't comment personally. None of these scopes are really high quality (aside from the Mueller, which I would say is sort of in the mid ground), but you may well be quite satisfied.
As for rings, I like steel rings. They are hard, tough, and the screws can be tightened properly without stripping. There are others, but I can say I've used Leupold and Burris rings and am very satisfied with them. Some of the 22 scopes come with rings, such as the one's you typically see under the counter at Walmart and Canadian Tire.
If you have the budget, get something good right off the bat. If not, buy something to get by, and save some money until you can afford something that will do that nice rifle justice. It should be a real tack driver. If its got iron sights, perhaps shoot with those until you can afford a good scope and rings.