Pam, we are sure JetPack has nice features and all but it allows you to add a blog / comment subscription module only. On the other hand services like MailChimp and Aweber are professional email service providers offering many powerful features which allow you to really benefit from the email list you are building. As far as simplicity is concerned, we are slightly more inclined towards MailChimp, they have a great user interface even for absolute beginners, they have excellent documentation, and lots of resources to learn how to use each feature available.
Before you can send AWesome emails with AWeber, you'll need someone to send it to. The easiest way to begin building your list is to import contacts that have opted-in to your email list, or gave you permission to send them emails. These could be subscribers you've emailed from another provider, or a list of contacts that you've built through your business.