I might state some things that are obvious. I don't know you, i will list even some points that may be trivial.
This also only applies directly to the rack, where i can say a couple of things as an IT guy.
Step zero for a move like this should be to verify that you have proper and working backups. Hopefully you have these anyway

If you remove harddrives, take note of their order, and to which machine each disk belongs. I had a server move where the dude responsible for shipping did not do that.

Luckily the backups were verified beforehand and worked, so no loss except a couple of hours for the restore.
I would also recommend unracking the servers. Not only can a fully stocked rack be too heavy, it also reduces the danger of losing everything in case of a mishap during transport.
If you cannot do that, you need to properly secure them. Screw down all rails. Click-rails can rattle loose. Remove all external cabling.
Depending on what machines you have, it may be sensible to remove more than just the harddrives. If you have long and heavy expansion cards i would remove these as well.
If your servers are custom built "whitebox" machines with heavy CPU coolers, remove those as well. With OEM rack servers that is gererally not required.
At the target location inspect everything before applying power. If in doubt, re-seat components.