The newsletter is something you can offer in addition to the normal follow ups. You can write a number of very short posts on news in the industry, summarise and provide links to the best articles over the past month, year and then add short mentions of products eg use your aweber and Bluehost affiliate links under a products I use section at the bottom.
The second thing you can do to is create an app in facebook for your webform. This allows you the ability to capture emails and promote your capture page using facebook ads. This is truly an autopilot strategy that the gurus talk about and teach to newbie and advanced marketers alike. Personally I have never done it like, I just know it’s easy to do because a lot of small and local businesses have it set up this way with a basic form.
I have used both, and I agree with your analysis. The great thing about MailChimp is that it lets you see the email in different clients. That is really the hardest thing about sending emails. However, you can use that service without doing everything else through MailChimp. Also, once you get the hang of it and develop templates, it no longer is much of an issue.
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.