Laptop with telnet software, Wireshark (or other Protocol Analyzer software or dedicated box)
Cat 5 cable (or whatever cable they use these days - I've been retired for a while) to connect directly to the switch or router from the laptop. Perhaps a serial cable (and USB- serial adapter) or USB depending on the switch or router or whatever is required to program them)
If using Cisco gear then a copy of Cisco Works or whatever they are using these days if you need it.
Power Strips! Surge protectors. UPS for the servers. Cat 5 cables to connect UPS to switch. If wireless access point is located in a different area you might want a separate UPS for it. You will need cat 5 cabling between the switch and the wireless access point
Rack (What earthquake zone is this? Requirements vary as to mounting.)
Cat 5 Cable Tester (unless everything is wireless which is unlikely.)
Tools perhaps including rechargeable drill and bits and mounting hardware if you have to install racks. Include spare RJ45 terminations, bulk wire, crimping tool. Or lots of premade Cat 5 cables.
If fiber required special tools and rack and make sure you have enough jumpers.
Drawings showing equipment layout.
Drawings showing room layouts.
Assurance of adequate AC in server room.
Assurance of physical security in server room.
Assurance of adequate power in server room (must support the servers and the UPS - some UPS require special 20 Amp circuits with odd wall plug)
Assurance of 24/7 access into building and server room. If not then must know hours access is available and who to call if access denied.
Assurance server room floor can handle weight of UPS, servers and racks.
Some means of remote access when the network is down. Do they still use telephone lines and modems?
Networking scheme. ISP info (passwords etc)
Some areas require all work be done by union members or at least that a union member be present so ask.
Probably need a printer in the office. Sometimes they use an All-in-one and sometimes they have separate printers, fax, copy machines and maybe two printers - one for color.
Manuals on the switch, wireless access point, router or at least the username/passwords.
If you are responsible for programming the servers then you need any additional software and if they are already loaded you need passwords.
You might also need some spare hard drives, RAM, and perhaps even a spare PC and spare server.
Personally I would stage everything in the lab, then break it down and ship it out to the remote location.
If you are in charge of the network after it's up then I would add one of the programs here so you can watch for bottlenecks and problems: