In general, you halt the upstream device first then work downwards. So, I'd first Shut down the hosts connected to the FAS270c. Then, halt the controller and power off. The last step, power off the disk shelves. After the move, when you power up the system, reverse the order.
The key is to use the 'halt' command when shutting down the FAS270. This turns off the NVRAM backup battery. If you forget, the battery will hold a charge for up to 3 days (probably less on an old FAS270 unless you've replaced the battery recently). The system will boot up and complain about a 'dirty shutdown', run some file system checking processes, and then come up fine.
Be sure to label the ends of all cables before moving. taking pictures also helps to ensure everything is reconnected fine. I always boot into maintenance mode after a system move. This way I can check the health of the system and fix any problems before Data ONTAP boots up and complains if something is wrong.