What should a first-time buyer get for paper targets and plinking?

A .177 break barrel in the 8 to 12 FPE class, or a quality multi-pump like a Benjamin 392/397, will plink happily for years with no fill equipment.

If budget allows and you want maximum ease and accuracy, a regulated .177 or .22 PCP plus a hand pump is hard to beat. CO2 guns are also excellent for casual indoor or backyard plinking. Avoid the highest-velocity magnum springers as a first gun; they are loud, hard to cock, and unforgiving of poor technique.