if that's any consolation.
It's certainly true that the router will have to be connected to a computer, but only for the short time it takes to configure it with your ISP login details. Once that has been done, you can disconnect the ethernet cable that connects router and computer and leave the router to do its job. Each time you turn it on (you should always turn a router off at night, when you've finished with it) your router will automatically make the connection to your ISP.
All routers come with an ethernet cable specifically for use during configuration, and you can use any computer for that process. It does mean that if you have only one PC you'll have to move it near the router temporarily. It's obviously necessary for the computer to have an ethernet card installed, or an ethernet port that connects directly to the motherboard, but pretty well every computer has one or the other.