My first job out of Uni was as a designer with an email marketing company
As suggested above, the best is probably Mail Chimp- and it's free up until a certain amount of emails (I forget how many, but it's a lot).
However, it (and most of them) can be a little daunting if you're not IT savvy (to an extent) or have a background in design.
MY BIGGEST advice would be to not bother doing any until you have lots and lots of people to email to.
The "conversion rate" on email marketing is pretty low to be honest (since spam filtering became more aggressive and frankly people have become more "used" to email spam and ignore it)
If it's something you're really keen on doing then spend lots of time "harvesting" email addresses before you even send your first one out.
Honestly? If you're not emailing a few
thousand people. It's not worth it. You're best sticking to normal marketing and social media.
We use it, but we've been adding to our mailing list for over 7 years- it's still not the most effective way of marketing for us either. It's just a "bonus".