50 emails per minute is 72,000 emails per day!!!! There is no shared host that is going to let you do that. You absolutely need a VPS or dedicated server for that volume of email.
You're probably just going to have to monitize the newsletter some way so you can afford a VPS or dedicated.
You can also try mass email services like Mailchimp (http://mailchimp.com/pricing/), but they are usually quite expensive.