We’ve changed email marketing from iContact to MailChimp and, just now, Aweber. We changed from iContact to MailChimp to cut costs. We then switched to Aweber because Mailchimp will not allow you to start an Autoresponder series on an imported list PLUS, as you mentioned, Aweber has much more robust measuring/management tools. However, people should be aware that Aweber requires imported subscribers to opt-in all over again.
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.