Purchasing a reconditioned or renewed router is cheaper but does carry notable security risks. Firstly the router may use firmware that is no longer supported or updated by the manufacturer which makes it vulnerable to having discoverable backdoors. Malicious agents may supply you with a router that has firmware that monitors and steals your data. They may even have tampered with the hardware.
Reputable second-hand routers have usually been through a factory reset and you can download and install new firmware from the manufacturer yourself. Buying a brand-new cheap router is always the safest option.