There are tons of free php apps for this, Check out sites like hotscripts like this one of many, many examples:
QLAP
also phpscripts is a good site: The PHP Resource Index: Complete Scripts: E-Mail Utilities , and my favourite php site, by far - Welcome to the PHP Classes Repository - PHP Classes
Here is an example of a php blog that incorporates these email functions you wish:
Pivot
I use it above wordpress, or any other.
If you can be more specific, we can find the exact script you want. Do you want double opt in? Cancellation option on every message?(This is highly professional).
Composing and designing your own emails is easy to find, as well as any functionality you desire. I can search some more if you still need help! I love doing this type of thing, for it is a vessel to learn about what is available and offshoot options.
First, what server/host do you have? What are the email types included?
Bye for now.