I am beginning to look for air rifles and scopes. Recommendations?

The answer depends entirely on what you want to use the air rifle for. If silhouette is your game then there are three classes of airgun you can use. Check the rules and see what floats your boat. Scopes are similar to smallbore scopes and you want one that can focus down to at least 20 yards for silhouette. generally try to stay away from cheap and really powerful guns. Buy the best you can afford.

The best advice is to go to a few matches and shoot complete matches with other folk's rifles. There is so much variety out there that you cannot purchase an air rifle without trying that particular model first. My wife is 5 foot 3 inches and prefers the club model Anschutz 8001 with the rubber recoil pad and Leupold 6.5 to 20 X40 EFR scope. She shoots this rifle in both Open and Target divisions. For Sporter she shoots a Beeman R7 with a UTG 3 to 12 scope because the R7 receiver is so short that it limits you to short scopes. She picked the R7 for sporter because by the time she shoots Target and Open on the same day, she is fatigued to the point that she wants something easy to cock and light in weight. Good air rifles are expensive but you have to remember that there are air rifles being shot every day that are well over 35 years old. When you spread the cost over the lifetime of the rifle, it is cheap. Most people here will suggest that you buy a 10 meter Target division rifle first because they are high quality and can be shot in both target and open divisions. Make sure that whatever you buy is easy to put a scope on. Some 10 meter rifles make it difficult to install a scope because of the cocking arm or loading gate hitting the magnification adjustment ring or the windage knob.