Mail server for the site

A few days ago there was such a situation that the hoster began to disable the site for a large number of outgoing messages. The client has a real estate agency, a rather high popularity of the site and many subscribers by mail. In general, about 2k letters are sent daily to subscribers. It is clear that today the RSS is a de facto standard, but not all subscribers will agree to switch to it. He categorically refuses to change hosting. There is an idea - to buy a server and turn it on for a couple of days a week. And, therefore, there was such a question. How can you configure the server, what would it send letters, what it needs to do ... What would it be attached to the main site. The designer himself, so I don’t understand the settings of the servers, but I hope I’ll know more soon. Interested in any useful information on this issue, useful links. If you miss something, ask.

ps like I'm writing to the right blog ...