A mobile broadband connection gets the broadband over the cellular (mobile) phone network, and will require some form of mobile phone type connection including a SIM either on a monthly or Pay-As-You-Go type contract. It will normally require you to install a cellular data dongle into a USB port on the laptop, and the dongle will carry the SIM card. This can have a range of several kilometres from the nearest cellular mast and will connect to any available mast for the chosen network that is within range.
Wireless LAN, normally refers to Wi-Fi, which is provided by a home router, a free Wi-Fi hotspot, a wireless access point, or even a hotspot enabled on a mobile phone. Wi-Fi has a maximum range of around 100 metres. For home use, this requires the home to have an ISP connection over a phone line or cable.
Unless you have a cellular dongle that you are using, then wireless LAN should be the option to choose.