This may be the easiest part of your server move.
How do I move Big Medium to a new server?
Make a copy of Big Medium's data directories and each site's document and image directories as described in "How do I make a backup of my Big Medium data?"
Install a fresh installation of Big Medium on the new server, and follow the setup wizard until you are prompted to create your first administrator account. Stop there and proceed to step 3 below.
Upload the data, document and image directories as described in "How do I restore a Big Medium installation from backup?"
IMPORTANT: If the directory paths for your site(s) have changed with the server move, follow this additional step before rebuilding the pages and style sheets as described in the data-restoration instructions for step 3:
Sign into each site and go to its "Settings>Site URLs and Directories" screen, updating the directory paths for the homepage and page directories as necessary.