The best way to have a wired internet connection in Linux, is by not using the USB port of the router/modem to connect to Linux. You would use the ethernet card in your system, if you have one, to connect to the router. Then the internet connection should work fine.
But, you did not answer any of my questions about your setup, so it's impossible to know what you have in order to answer your questions.
Wireless is a little more tricky, depending what card that you have, if this is a wireless setup. In windows, your ISP usually gives you a setup disk to do the job for you. In Linux, you usually have to do it manually, so knowing what you have determines how easy it will be to set up the connection.
However, your last post says it all. If this system is used by the entire family and say you deleted Windows in favor of Linux (without having an idea how to set up the connection), then I can see your father's point.
It would be best to have a second system that you could play with and learn Linux. Then you can convert the family by showing them how it works!

You can have both Windows and Linux on the system, but I would not recommend this, as it seems that you don't know enough about the process to mess with the family system.
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"I love it when a plan comes together." - Hannibal Smith