We have a website that requires to send 1000+ emails a day to all the customers who opted for the alerts. In couple of months time we are expecting to raise our customer base to
If you can't or don't want to install your own mail server, then one option is to lookup the MX records for the destination mail servers, and do the delivery directly from your application using the SmtpClient class.
Ideally, you should do this from a background thread (a Windows Service would be even better), to minimize interference with the rest of your web site.
IIRC, MX DNS lookups aren't available as a standard Framework call. However, they are pretty easy to add using p/invoke.