If you're sending large quantities of e-mail, you need more than a desktop program. Outlook or Thunderbird will quickly bog down.
Instead, you need a program that runs off your Web server. E-mail management programs are relatively easy to find. But they're not for the faint of heart. They can take quite a bit of work to set up.
Majordomo is one program that will help you manage your mailing list. Once you set it up, you can manage lists via e-mail. There's also an add-on Web-based management tool.
Before you get started with Majordomo, read the instructions and FAQs carefully. Make sure you have exactly what you need to run it before you install it. This could save you a lot of hassle in the end.