We use Mailchimp and generally find it easy to use and with its own analytics, although the recent updates have caused some confusion. The newsletter is contained in the body of the email so our open rate is based on who opens the email.
We keep our notices/articles brief with timely updates and reminders and all contained in the body of the newsletter, with no links to ‘read more’ as this tends to lose people (and we use other publications to cover more lengthy topics). We only provide links to extra info e.g. videos, websites, forms, attachments.
I think the important thing is knowing the purpose of your newsletter and not replicating other comms. Readership stats will give an indication of engagement and whether the content is hitting the mark. Depending on your comms mix, a newsletter may or may not be important.