Cable customer? You need a router.
ADSL customer? You'll need a modem/router.
That's it, basically. Your desktop is 99% sure to have an Ethernet port (RJ45) unless it's quite ancient in PC terms. No point using a desktop wirelessly unless your router has to be some distance away, beyond practical cable range.
Browse the Networking forum; read recent similar posts and note the advice that I and others have given. It applies here as well.
If you want specific advice about which router to buy, let me know.