Not really as each is a case by case basis.
1. Get your pipe up on the new bldg 1st.
2. Of your major servers, you should have a comparable "clone" and full backup of those servers, for those just in case issues (Someone banged the server in shipment and inop now).
3. Install spare rack, network boards and install a couple of new switches (spare ones if you have them, just enough to connect your servers and about 20 workstations). That way, worse case scenario, your servers are up and the important people are up to conduct daily business.
4. Hook up your gateway box and test your lines prior to moving servers.
5. Move servers preferably on a weekend, or whenever the most downtime is allowed. Ensure you do the full backup on all. Connect the servers and redo your routes.
6. Change firewall rules / dns if need be for new line. Test away.