Metallic silhouette shooting will satisfy that need to see something react when hit. There are 3 classes for rimfire, bolt action hunter style rifle, target rifle bolt action, and lever gun shot at 40, 60, 77 and 100 meters. In the rimfire lever gun class you naturally can use a lever gun but a pump action or a semi auto can be used but must have a tubular magazine. Scope for the bolt gun class and iron sight in the lever gun class. All shot from the standing unsupported no sling allowed position. Silhouette is a difficult competition and a lot of people who try it out don't come back after their first or second match, their ego is too delicate. You don't need high dollar equipment to get started but you need a scope with target turrets to adjust the settings for the different distances. It will surprise you how many places there that shoot silhouette, go to steelchickens.com and peruse the forum. There are lists of clubs that hold silhouette competition.
There is also pistol cartridge lever gun class, big bore lever gun shot out to 200 yards and high power bolt gun at 500 yards. There is also handgun silhouette in rimfire and center fire, iron sight and scope. Something for everyone. I shot benchrest for a number of years and punching holes in paper gets old after awhile, silhouette is a lot more fun.