I was a network engineer for far longer than I care to admit...
, but I've been able to use that experience to help with migrating my sites.
I have moved up to 50 sites at a time (kind of forced to), and I've done it several times. If you do these steps, you should have no problem:
1. upload all sites to new server. don't change anything for now, just upload an exact copy of all the sites to the new server.
2. Make sure you have databases, email accounts, etc. running on the new server. Print the documentation out, it helps.
3. Take your least important site and change the NS on it. That way, if there are any problems, it doesn't affect the most important site.
4. Test it, test it, and test it again. Get everyone in the office to test it. Test it for at least 3 days so you can be assured the new NS has propagated throughout the Internet.
(This has an added benefit if some of these sites are linked to each other. Google minimizes the importance of linked sites that are on the same IP. By taking your time to move them, Google will see them on separate IP's, and possibly raise your
PR and ranking. That happened on my sites once.)
5. Delete the site from the old sever, and test again. I've seen where broken code and improperly migrated databases worked because they were on the old site too. Sometimes linking will be by IP also, and you won't catch that until you delete the site from the old server.
6. Change the password. Not necessary, but recommended. One time I changed servers, and the people at the old datacenter didn't want me gone so they went in and changed the A records back to their servers.
7. Go to next site.
Hope this helps!
Ty