If your users will sign up and confirm and you are not just adding people on your own I would use one of these as they have 15-60 day free trials to get the hang of it and the templates they provide don't take much to tweak to make them look pretty sharp. I have used constant contact in the past and it was pretty simple. Haven't used any of the others but I got a new site that could use one so I might eyeball one of the others for a comparison to my Constant Contact experience. Benefit of these is it sends from their servers so you will never have an issue with someone disabling your domain, worst case if you did some shady shit is they suspend your email marketing account.
Constant Contact 60 Day Free Trial
Campaigner 30 Day Free Trial
Vertical Response 30 Day Free Trial
iContact 15 Day Free Trial
Infusion Soft