I typically use 'Internet site with smarthost' for postfix running on my laptop, and specify my company's SMTP server as the smarthost. For a computer that doesn't roam between networks, it would be fine to specify your ISP's SMTP server as the smarthost. If you have a Google account, you could use Google's SMTP as well.
'Internet site' might also work, but it might run afoul of various spam protections, since it will try to reach each recipient's SMTP server directly.
I'm not sure what 'local' means; can you check (netstat -tln) if Postfix is even listening on 127.0.0.1 port 25? If not, Thunderbird won't be able to talk to your Postfix over TCP.
On the Thunderbird side, specify localhost as the SMTP server with no username or password.
