Integrating GetResponse autoresponder with Joomla CMS will definitively be trickier than integrating AWeber because it seems there's way less material covering GetResponse integration in general, including on their own site and support forums. There is no API or database integration. There are settings where you can email to a specific email (e.g. subscribeme@yoursite.com) and get added though which could probably be leveraged to achieve this.

Ideally, when a new member subscribe to your Joomla site, he would then be subscribed to one of your lists (or at least a confirmation email from GetResponse should be sent to his email address) and then later on he would have the choice of subscribing to more lists directly from your Joomla site.

Well, it's definitively not that simple, here's what I've found:

If you want to know how to email courses to your website/blog visitors, you need to take a course yourself!

What you need is an autoresponder, something that will automate the process of sending a sequence of emails to any number of emails.
Here are the two main players in the email marketing field. Those two companies can ease the process for you by taking off your mind any technical problem that can arise from sending many emails regularly.

So... how to email courses? Subscribe for free to each of them and learn from their email course dealing with tips on how to do email marketing. And later you can decide which one gives you the best bang for your buck!