The malware that Joseph is working to counter has copied itself to workstations across his environment due to a central, shared fileshare. What type of malware is Joseph most likely fighting?

Joseph is most likely fighting a virus, which is capable of copying itself to new locations. A Trojan is malware that is disguised to look like desirable software, a keylogger captures keystrokes, and a rootkit is intended to allow attackers to retain access to compromised systems.