How can I change the default encoding type Thunderbird uses when composing a new email?

Tools → Options → Display → Formatting → Fonts → Advanced... → Character Encodings → Outgoing Mail:

For Thunderbird 17 on the Mac, you can find this setting at:

Thunderbird > Preferences > Display > Formatting > Advanced

Look at the Character Encodings section, as seen here:

On Mac OS X you have to use the Config Editor (also know as about:config) found in Preferences -> Advanced -> General. Change the value of the preference named mailnews.send_default_charset to UTF-8.