Will it be "Mac to Mac" or are you switching platforms?

Firefox normally stores your bookmarks in a database along with your history. It allows you to create bookmark files in two different formats. I suggest creating both:

• JSON-format backup, more complete, but barely human readable: Restore bookmarks from backup or move them to another computer
  • On your new Firefox, you would use Restore to replace the existing set of bookmarks with your backup

• HTML-format export, readable by loading into a browser, cross-browser compatible: Export Firefox bookmarks to an HTML file to back up or transfer bookmarks
  • On your new Firefox, you would use Import to add these to your existing set of bookmarks (if Restore of a Backup does not work)

You can save these files on portable media such as a USB flash drive, or in iCloud or other cloud storage, or email them to yourself, or all three.

Make sense?

Of course, if you previously set up Firefox Sync, you can add your new computer (your new Firefox) to your existing Sync account. There's a section in this article on that: How do I set up Sync on my computer?