You can copy files like these to the current Firefox profile folder to recover specific data.

• bookmarks and history: places.sqlite
• bookmark backups: JSON backups in the bookmarkbackups folder
• SQLite files like cookies.sqlite (cookies) and formhistory.sqlite (saved form data)
• logins.json and key3.db (decryption key) for Passwords saved in the Password Manager
• cert8.db and possibly cert_override.txt for (intermediate) certificates stored in the Certificate Manager
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other Site Preferences
• sessionstore.js for open tabs and pinned tabs and tab groups

You can use this button to go to the current Firefox profile folder:

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox

• https://support.mozilla.org/kb/Recovering+important+data+from+an+old+profile
• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

See also:

• https://support.mozilla.org/kb/Backing+up+your+information

"Would creating and singing in to a firefox sync account cause me to lose my existing bookmarks list? In other words, when signing in for the first time, does it actively sync to a blank account? " No bookmarks will be lost. But if you have an extraordinary large number of bookmarks, it will take some time for Sync to get them all.

The initial Sync process will send all your data on the older PC to the Sync server, but sometimes it may take a few hours to get everything. So don't rush when setting up Sync on the new device.

Quite honestly, if you haven't used Sync before the process of "transferring" your data as cor-el mentioned might be your best cource of action, though. There is a bit of a "learning curve" to using Sync.