Over 350k subscribers

I have over 350k subscribers to an exact product. I want to start new website with the same product and I'm interested as to get the maximum from subscribers and monetize. What is the best way to use that email address and get the best results? Which service is best for email marketing right now?
Should I try it with some VPS and set smtp myself?
I'm not in a hurry and have some time even sending 500 emails from gmail accounts daily but I want maximum results. Please any advice is welcome!

Thanks Polo0
MailChimp sound interesting... Has anyone tried it?

Someone....

I have an idea, I have material, I have a target audience.
I'm a total beginner and need your help to do this the right way. Please advise...