Does jotform make a list for me of people who have signed up ?

You can see that in your form submissions view: https://www.jotform.com/help/269-How-to-view-Submissions 

You can even setup email notifications, so you get one each time someone submits your form:

http://www.jotform.com/help/25-Setting-Up-Email-Notifications

Let us know if you need more help.