Connecting 2 computers differently to modem

My son has a modem that can be wireless or cable. He mostly uses it via cable, but can I set up my wireless computer to use the modem at same time or would he need to have the modem set to wireless? Failing that, could I set up a second modem as a wireless one just for me?
I am new to wireless computers and technology, and I need another computer, so I wanted to know what I could do before buying the products.