I've been using airguns in the garage for years.
No harm that I've noticed....that I've noticed......that I've......
What were we talking about?
For targets, I use 1/2 plywood boxes, about and inch and half deep, lined with carpet and rags, with cardboard facing, under the paper targets.
Some are ten years old, at least, and still hanging in there.
Don't sweat the lead pellets.
If they really bother you, use airsoft, although they aren't as accurate, more like a bb gun.
Lock the doors, they're coming in the windows.