E-mail advice for business newsletter? Paid or Free solution

Hey I’m setting up a business website for a client, just thought I would ask advice for best e-mail solution.

They have about 700 users on their newsletter list. And they send out an E-mail maybe twice a month.

They are hosting with godaddy but their e-mail is very unreliable, and you can only send to 100 users at a time.
Any recommendations to an email service that will allow use to send emails showing our domain name ([email protected]), and we can send to a bulk of people in one shot?

A free solution is great if it really works good. We don’t mind paying for a good service though.
Also is there some kind of plugin or extension on wordpress that may be an option? So they can log into the wordpress backend and go to their mail box from there?

Thanks in advance for any ideas.