Okay, I think I see now. It still sounds like an assignment, so I'm going to treat it as such:
Are the Annexe and the main building on the same subnet? If so, consider whether or not you'd need a router (hint: you wouldn't). What cables are you familiar with? The inside choice should be obvious, but you'll need something that's not susceptable to interferance and weather for the outside interconnect. How many hubs/switches would you need? If you've got a bunch of users, I'd recommend a switch, preferably one in each building.
...Are we connecting the VDUs? How do the VDUs connect? Serial? Can you use tranceivers?
Your question isn't complicated, but it is rather drawn out. It seems like a case study I did for a Cisco class a few years back. I'd concentrate on wiring the buildings first, then decide what method you'd use to maintain the interconnect between the buildings. Breaking down the problem will make things easier for you. My suggestions:
- Determine which building will have the Internet source coming into it.
- Determine which equipment (LAN gear, routers, switches, etc) are needed to wire that building.
- If building A has the Internet source, consider how to connect the VDUs to the mainframe, then the mainframe to your LAN.
- Determine how to wire up the Annexe.
- Determine how to connect the Annexe to Building A.
Those steps should take care of things for you-- it should be your task to choose what wire is appropriate.