What is the best and cheapest way of selecting the right pellet?
You fail to say whether your air rifle is spring powered, pre-charged pneumatic (PCP) or powered by carbon dioxide.
Most spring-powered air rifles work more efficiently with lightweight pellets, as do CO² rifles, while PCP rifles are more efficient with a heavy pellet.
These rules apply to diablo-shaped lead pellets but there are now pellets on the market of more advanced and aerodynamic design that will give efficient results in most air rifle barrels with regard to bore size, type and direction, pitch of rifling and whether or not the barrel is choked at the muzzle.
As a general rule of thumb, in spring-powered rifles the head of the pellet should be the same size as the bore or land size, and the skirt diameter should be the same size as the groove diameter of the barrel.
This is not the same for pre-charged air rifles, where the pellet is sized down to be an exact fit in the barrel when the pellet is chambered by the transfer probe.
In order to select the most efficient and accurate pellet for your air rifle you will have to test several different brands.