Hostgator (suggested by @Direct Webstore)
ONLY "
Hosgator Business Cloud". Their other options are crap.
But I have also set up an Intersever account and have moved 4 sites there. The other 4 are still on Hosgator, but I won't be renewing my account there. I will be opening a second Interserver account.
The main reason is price, Interserver gives the same results as
Hostgator Business Cloud at a much lower price.
The second reason is Interserver's built in free "Mail Channels" email server which saves even more money by not having to pay for something like Mailchimp. You can send up to 200 emails per hour, per domain, which is more than adequate.
As for bulk emailing of Newsletters and promotions, I have the free "Mailpoet" newsletter plugin which allows me to set how many emails per hour it sends. I set it to 100 per hour, which still leaves another 100 per hour for the transnational emails.