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 infrared light through an optical fiber. The light is a form of carrier wave that is modulated to carry information. Fiber is preferred over electrical cabling when high bandwidth, long distance, or immunity to electromagnetic interference is required. This type of communication can transmit voice, video, and telemetry through local area networks or across long distances.Optical fiber is used by many telecommunications companies to transmit telephone signals, Internet communication, and cable television signals. Researchers at Bell Labs have reached a record bandwidth–distance product of over 100 petabit × kilometers per second using fiber-optic communication.