I think the most important thing you should do is work with experienced and reputable movers. As this website shows, qualified NYC movers will know how to handle your equipment with care. They know the best ways to pack and transport sensitive items so damage is less likely.
While working with movers is key, it's also crucial that you label your equipment properly. Clearly marked boxes help movers know which items need extra care. Discuss your requirements with the movers ahead of time so they understand your expectations.
It's also smart to get insurance for your more valuable equipment. This extra step can provide peace of mind. No one wants to deal with broken equipment, but knowing you're protected can relieve some stress.
Your moving company will likely offer some type of insurance, just make sure you're getting enough insurance to satisfy your needs. A policy that pays only based on the weight of the items damaged won't be enough to cover expensive workstations or bespoke workshop machinery.