Used Mini-14 or Ranch Rifle. If you can get one in stainless (and you can for WELL under $600) that hasn't been run over by a truck, it will serve you well. It remains a great centerfire plinker, despite match rifle fans' complaints about its lacking long-range target accuracy.
Used Marlin Camp Carbine. They don't make them any more, but they used to make them in 9mm, which is a great plinking round because quality ammo is readily available for cheap, and because its range is limited. You don't need or want a 1000 yard cartridge for plinking. It makes it harder to find an appropriate place to plink.
Ruger PC9. Little Police Carbine in 9mm. Also available in .40, but that's more expensive to shoot. The PC and the Camp Carbine can double as defensive arms for home or campsite.
Olympic Arms Plinker. A no-frills AR-15 for under $600. Some people don't like Oly's. Some do. Gun Tests seems to like them, and that's a positive thing. Maybe your best bet.
Of course, the .22LR is still the king of plinking, because it's cheap and accurate. Many good rifles are available in .22LR, most are less expensive than centerfires, and it's also not an overpowered round that will travel much farther than you intend.
