Because your traversing different levels, wireless is out. Coax isn't practical to begin with, so that leave Ethernet and Fiber. The question specifies this is a large building, with a large network, so fiber is the best choice.
Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of light through an optical fiber. The light forms an electromagnetic carrier wave that is modulated to carry information. Fiber is preferred over electrical cabling when high bandwidth, long distance, or immunity to electromagnetic interference are required. This type of communication can transmit voice, video, and telemetry through local area networks, computer networks, or across long distances.
Optical fiber is …