Hey Elizabeth!
The most common newsletter service we typically work with is Mailchimp. Though it may be a bit complex, it does set the standard for online newsletter distribution and functionality. Furthermore, most of our themes integrate directly with the Mailchimp Form Action URL hookup that allows folks to sign up for a newsletter from Mailchimp directly from the storefront. We also have the great Chimpified app which will pull customer information over to Mailchimp after a customer orders and opts in for email marketing, even if they don't sign up for the newsletter separately, too.
http://apps.shopify.com/chimpified
Though Campaign Monitor is also a good platform, we've found most people tend to prefer Mailchimp. Though, it's quite possible someone else may chime in to this thread with an equally compelling argument for Campaign Monitor.
Ultimately, we want you to be comfortable with whichever service you choose to go with, and so I might suggest trying both out to see which suits your needs better.
Talk to you soon!
Matthew Buttler
Guru
Shopify Inc.