Email, ASP Timeout And Web Host

I'm sending emails to a database of 2000 people (that will be double
that in the future). My web-host provides ASPQmail. I have to send the
emails out in groups of only a few hundred at a time to avoid the page
timing out (I have set the timeout value to a very high value). Once in a
while it seems as if either the SMTP server or the web server is running
slowly and I can't get it to send even a few without timeout problems. I
never get the log file showing anything.

Is there a better web-host situation and email/SMTP I should look for?
Do I need a dedicated server? Any suggestions as to how to go about a bulk
email scenario? At least when I do have problems I would like to know
which clients received their mailing and which ones didn't.