Many companies offer a large variety of rifle scopes with a different field of view and power optic lenses. The cross hairs is the most commonly used site picture when looking through a scope. But there are many other styles.
The scope you choose will depend on the caliper and velocity of the rifle and the job it is intended for. The 22 rimfire rifle is the 22 caliper that has less velocity than some of the center fire 22 calipers. It is generally used for small game hunting like squirrel or family fun of plinking backyard targets. The most common scope used for this rifle is a standard 3x or 4x power optic lens scope.
The 22-250 rifle is intended for long range varmint shooting or long range competition shooting at the local gun range. The proper scope for this application would be a 6x23 or 4x18 power optic lens scope.
Some of the rounds intended for large game are the very popular 30 caliper which is the 30-odd 6 rifle, an American's favorite, because of its versatile use. It can be used as a short range brush gun for hunting white tail deer in the back northwoods of America or as a long range rifle when shooting pronghorns in the northwest part of our nation. The scope would be chosen depending on the application it is intended for. A 3x9 power scope is commonly chosen for this rifle.
Very large game rifles such as the Remington 416 is commonly used for cape buffalo or African elephants. This rifle is never equipped with a scope because of the recoil and muzzle jump of the rifle due to its powerful cartridge. It is believed that these rifles would cause damage to the optics in a scope if mounted to this rifle.
When choosing the right rifle scope, be sure to pick one that has been designed to be water tight and fog resistant. A good quality scope is assembled with a gas inside to prevent the lenses from fogging up. That's why you never disassemble a scope--that would release the gas needed to prevent fogging.
Many other rifles with popular calipers are used in hunting, sport shooting competitions, and recreation. It's important to know what your rifle is capable of and the application that it is intended for to make an intelligent decision when choosing the right scope for your rifle.