The mail server for the site

A few days ago there was such a situation that the hoster began to turn off 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 mail subscribers. In general, about 2k letters are sent to subscribers daily. It is clear that today rss is the 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, such a question arose. How can I configure the server so that it sends letters, what needs to be done for this ... That it would be tied to the main site. The designer himself, so I’m not good at server settings, but I hope I will know more soon. Interested in any useful information on this subject, useful links. If you missed something,

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