I have a HP 6 yr old tower home PC, and a3520 printer connected with cable

So now the black ink doesnt print(i looke d it up online and tried to unclog with alcohol and water as best i can as the tray is not detachable and i changed toners carts)....so I am going to buy a cheap printer like this one.

They all say "wireless". Does that mean they give me something to plug into the port of the computer(where the printer is currently plugged in) that sends a signal. Or does the computer itself have a transmitting signal internally? Not sure how the wireless portion works. Since its 6 years old will wireless be ok with this windows 7 HP.