What is the best way to move a project from an old device to a new one?

You have different options:

1. Export the project as a JSON file and re-import it on your new device.
2. If you use iconfonts and you need to preserve unicodes, you can export the project as an icon-font file and re-import the .svg font file. When importing the font file, make sure to check the 'Copy icons to project' option: this will automatically create a project for you, preserving the unicodes.
3. Sync your icons on your two devices.