An airgun by itself isn’t of much use. The first thing you need is a good selection of pellets. There are hundreds of pellets on the market in various shapes, sizes and weights. A good many of them are actually pretty useless. Many are being produced on machinery so old that the dies have become worn, and the pellets are oversized. Some are not appropriate for the guns they’re being marketed for. One example is the Beeman Silver Jet, a delicate pointed pellet with fragile skirts designed for very low power Japanese pneumatic air guns 40 years ago. It should never be used in guns with more than 4-5 foot-pounds of energy.
Useful pellets can be divided into two groups: Flat nose (wadcutter) pellets for target use, and round nose pellets for everything else. Flat nosed pellets are used for target shooting because they cut nice round holes in the target. That’s it. Use them in target guns, or for informal target shooting with low-powered airguns.
Round nosed pellets have better aerodynamics for longer distance shooting. Keep in mind that Olympic air rifle competition takes place at only 10 meters; everything farther than that is long distance shooting in the world of air rifles!
You can also buy hollow point pellets, which are supposed to expand better (they do not, at least at typical air gun energies), pointed pellets, which are supposed to penetrate better (they don’t, and have poorer aerodynamics) and a host of other designs. Most hollow point pellets, like the Beeman Silver Bear, are really just round nosed pellets as far as performance is concerned.
There are really only three factors your should consider in selecting pellets: Size, consistency from pellet to pellet, and weight. Size means more than just selecting the right caliber. Some pellets are undersized, which leads to blowby, which reduces accuracy and can damage high-power spring guns. Some barrels may run a few thousandths larger or smaller than others. Some pellets are available in a range of sizes in a given caliber, and serious Field Target competitors spend a lot time testing to see which work best. .177 caliber Air Arms Diablo pellets can be had in 4.51 and 4.52mm, for example.
Consistency leads to accuracy- you want each pellet to be like every other pellet. Mass influences the transfer of energy from the gun to the pellet; for every gun, there is a pellet weight that will provide the maximum energy transfer, and a pellet weight that will produce the best accuracy.
Spring guns in particular are very sensitive to pellet weight. Too little, and the pellet will leave the barrel before it has transferred all its energy to the pellet. This results in the piston slamming against the front of the chamber, which in turn leads to poor accuracy, higher perceived recoil, and shorter piston seal and spring life. Too heavy a pellet leads to loss of power. The best way to select a pellet is to find out what other shooters are using, and use that as a place to start experimenting.
That having been said, I (and others) have found that Crosman Premier pellets are among the most accurate and consistent pellets currently made. The .177 caliber pellets come in two weights, 7.9 and 10 grams, and one should suit most field guns from 10 to 18 foot-pounds. The .20 and .22 pellets are very good as well. Many Field Target shooters and hunters are now using the aforementioned Air Arms pellets in .177 and .22. Target shooters should look at the wadcutter pellets from RWS and HN, both of whom make wadcutters in different weights and levels of quality.
Update: Since I wrote this, JSB pellets have become me available in the US from Pyramyd and other suppliers. Like Crosman, their pellets are available in a variety of weights, but they go a step farther and also offer a number of different diameters in each caliber. This has been common in flat nosed match pellets, but until recently wasn’t seen in round nose field pellets. If you’re a competitor this allows you to choose the pellets that will get that last ounce of accuracy out of your gun.