[gregjor]

I have used both Mailgun and SendGrid on projects with similar numbers of outbound emails and both work as expected. I had slightly less trouble working with SendGrid. I have never seen any problems with their dashboard. You can use their API libraries, or just send a direct HTTP request, or have sendmail on the server configured to relay through SendGrid.

You can also relay through a GMail account if you already use GMail for inbound emails on your domain.

Having done this a few times with various web sites I can say it takes less than an hour to integrate MailGun or SendGrid and get it working. You probably don't want to implement and manage an email server and bounce/unsubscribe handling yourself.