Hiya,
It all depends on how you have set it up :)
Its probably easiest to migrate to the same ZAP and Java version, and then update those afterwards if you need to.
How will typically want to copy everything under there to the new machine.
But you will need to look at how you are using ZAP.
You can reference things like automation plans and scripts that are anywhere on that machine, or even a mounted network drive.
Cheers,
Simon