Okay, Verizon is your internet service and email provider, but they are the service carrier, not your email client program. Verizon provides the service but you have to have a program such as Outlook Express (the most common email client most people use prior to Vista since it comes with windows by default) to access that service and receive your emails.
My concern is that Mozilla usually automatically imports server settings from Outlook Express (OE) during the installation, and if it didn't and couldn't find them, that means OE probably isn't your email client. In fact if memory serves, I think they did away with OE in Vista and went to "Windows Mail" or something like that (I've used Thunderbird since I was using Windows XP and have never used Vista's email client so I'm not extremely versed there). It would really narrow things down if you could find out what your email client program was then I could give you more specific information.
I have never used Windows Mail, so if that is your client, it may be very different but try these instructions and see if they point you to the right area of the program.
To find your incoming and outgoing POP3/SMTP servers, open your email client and click on tools at the top of the email client window, then scroll down the list and you should see "accounts" or something similar. Click on that and you should see a window with your name, or your email address on the left hand side. There should be a "settings" button on the right or something like that, or you should also be able to double click on the name or email address in the pane. That should bring up a window listing your incoming and outgoing SMTP servers. (Something like mail.verizon.net would be my guess). Copy those over to Thunderbird, enter your password to access your email accounts and tell Thunderbird to save it, and you should be up and running.
I also did some digging for you and found an extended tutorial blog with a full
walkthrough on setting up Thunderbird that may be helpful.
Once your done and have the servers set up and your email working, let me know and I'll help you export your emails from the old email client to Thunderbird if they didn't move over automatically as well.