I strongly recommend Constant Contact. I've been using it for several years and recommend it to all of my clients. I've even recommended for our town's Little League, schools and recreation program.
It is easy to use (with a little bit of practice). The emails look great (plenty of templates). And you get a complete report on opens, click-throughs and bounces. Not only do you get a number, you can see who actually opened, clicked through or bounce - so you can follow up if you want.
Pricing starts at $15 a month - based on the size of your list, not how often you send emails. It's the same price whether you email once a day or once a month.
Constant Contact is one of dozens of self-serve email systems out there. Others include iContact, Aweber, Vertical Response. All are pretty much in the same price range.
You've already seen a Constant Contact demo, but here's the link anyway:
Let me know if you need any help. Good luck!