Wi-Fi works based on your laptop or your desktop’s wireless ability, if they have that kind f feature. Normally most of the laptops, you would find wireless networks and features available, but in case of a desktop system you might as well have to buy and install an NIC card with wireless features.
Yes Wi-Fi normally is cheaper than broadband but then again it depends on what plan and bandwidth you are plannning to take. But there is a catch that you will always find a lot of variance in the bandwidth in Wi-Fi because it is wireless, but in case of wire-line it’s dedicated. But anyways both are a fair choice to make.