If I buy Toshiba with the built-in high-speed wireless LAN, will I need anything else to buy?

If the current device that terminates your Internet connection does not support wireless connectivity, you would need to replace it with one that does or alternatively add a wireless access point to your wired network.

Thank you very much for the answer! Do I talk to the cable provider?
Sorry, but I am 70 years old and my grown daughter moved in with me. I definitely need to buy her a laptop since there is constant jockeying for the chair in front of my PC. ((