Full disclosure: I work for AWeber. But I would definitely consider us as an option for your client.
With AWeber, you have the ability to create your own HTML templates or use our drag-and-drop template editor for something more simple and easy to use. It's perfect for someone who's not looking to do anything too technical. You can also code a template that your client can use in the drag-and-drop editor.
There's no extra fee for analytics and reporting - our pricing tiers go by list size. And we have amazing customer service that's available via phone, email or live chat 7 days-a-week.
If you have any questions, you can reach out to me directly. I'd be happy to help!