Email newsletter signup non members

Hello. I realize there are many plugins to add a newsletter to WordPress but what I need is to allow users to enter their email address into a custom form I have set up in my footer.

The site does not take member registrations or anything like that. How would I go about setting up so site visitors can simply enter their email address into my form, their email address gets stored in the database and the newsletter gets mailed to anyone with an email address that has been inserted?

If anyone knows any good newsletter plugins compatible with this that would be sweet as the deadline for this project is looming.

Thanks for any help/ideas