I prefer simple and unobtrusive notifications (if such notifications don't defeat their own purpose!) and found just what I was looking for in the Ubuntu sound files (have a look in: /usr/share/sound/ubuntu/stereo). The problem was that the file was an .ogg format and Thunderbird prefers its noise in .wav files. Fortunately it's easy to fix audio file formats using FFmpeg.
If you don't have FFmpeg on your system, open a terminal and type:
sudo apt-get install ffmpeg
ffmpeg -i /input_file.ext /outputfile.ext
For instance, I wanted to change the message-new-instant.ogg sound file to a .wav format, change the file name to "mail", and save the converted file somewhere convenient. My code looked like this:
ffmpeg -i /usr/share/sound/ubuntu/stereo/message-new-instant.ogg /home/jogga/Documents/Sound/mail.wav
Note that my destination directory had been created prior to executing the command.
Now that the file has been converted, use the preferences browse button in Thunderbird to select your new .wav file and you should be notified whenever you get mail.
Sources & References:
FFmpeg Home Page