How many proxies do I need???

So if I want to send out responses in batches say 200 at a time using like 20 different gmail accounts/smtps with Easy AutoResponder how many proxies will I need? Can I use like a shared proxy account from proxybonanza that they offer like 8 IPs for $6/mo and rotate like every 20-25 emails?

Or for what I want to do it's better to get private proxies? For the shared ones if one goes down does proxybonanza just replace it with another so that I have 8 available to me all the time?