Sheet of wood. one layer of carpet stapled to it at the top, another stapled to the back of the top, then flipped over to the front so it hangs a little bit away, has some movement (which helps absorb any rebounds). This setup has been fine with 12ft/lb rifles.
You could just pin targets to this, but the bullseye will wear through fairly quick (you being an ace shot and everyhting, like me) so you might like to knock up a pellet catcher from a bit more wood; fill the back of it with plumber's mait which will hold the pellets that hit it (and be very quiet) - just fold it over itself when the pellets start getting dense. Or buy a proper one (usually steel-backed, will make a loud "ting" when you're on-taregt... can annoy the neighbours).