Competitive NRA Smallbore Rifle Silhouette target shooting should be done with rimfire ammunition designed for long range target shooting. If you are new to the sport and just want to try it anything you have confidence in is fine to start. The target type ammunition is typically wax-coated for lubrication. This wax coats the barrel over a period of shots and improves the rifles accuracy. The lower velocity ammunition along with the wax coating prevents lead buildup in the barrel.
Recommending specific ammunition for a rimfire rifle is almost impossible. The accuracy of the ammunition varies from rifle to rifle. To some extent, you get what you pay for. There is no way of deciding for certain without extensive study at the range. If you are new but want to use target rimfire ammunition there is no reason to dedicate a lot of time and money trying out ammunition. Buy anything affordable to experiment with it for a while. In the beginning your ability to hold and fire acurately will be the cause of more error than the ammunition. The better precision will be more important after you gain experience in the sport. After you get better at holding the rifle, the ammunition may cause you to miss some of the steel targets.
Competitive High Power Rifle Silhouette steel target shooting is done with hand-loaded ammunition with load designs tested by the shooter for the most accurate results. Many shooters use a smaller bore for thew lighter recoil. They use a a heavier bullet to shoot the heavy 50 pound steel targets of the Rams and lighter bullets and loads for the remainder. I estimate at least 900 ft-pnds of energy required to reliably knock down the Rams. The safest minimum is the 950-1000 ft-pnd range. Ringers are the nick-name given to those bullets which hit their mark but, the heavy steel target of the Ram remains standing. Those shooting the lighter bullets know the term better than I do.
Personally I use a Remington 7mm08 with 168 grain sierra Match King bullets. I use one load design for every animal. I was using Varget powder but due to lack of availability I had to switch to IMR 4166. It seems to be working well. It is supposed to be good for eliminating fouling and also is supposed to give similar results in various temperature ranges.