Power source: spring and gas-piston rifles are self-contained, PCP rifles are more accurate and quiet but need a pump or tank, CO2 is easy for plinking.
Calibre: .177 shoots flatter for targets and small pests, .22 and .25 hit harder for hunting.
Check the velocity (fps) with the pellet weight you plan to use; lighter pellets show higher numbers.
Airgun rules differ by state and city, so check local laws before you buy or shoot.