Low cost web hosting and email service are really two different things. I don't know of a web host that does a stellar job at email, and vice versa, most services that offer business class email don't offer web hosting or do so on a very limited basis. Things change when you reach the enterprise level of hosting (think Rackspace), but that's not low cost web hosting.
The specific problem that low cost web hosts all face is that they attract those wishing to generate spam. That is how servers end up getting blacklisted.
As a dreamhost customer, there are multiple options for generating mail via a script. You can simply send email from the web server using php's mail(). This is the email type that most often ends up getting blocked via an RBL. The second option is to have your dreamhost web server use SMTP to originate your email from your dreamhost email server. This method gets RBL'd less often, however dreamhost doesn't offer what I would consider business class email. Another option appears to be using a VPS or dedicated server at dreamhost for which SMTP Quota's don't seem to exist. This is likely because if you get RBL'd for your actions it's only going to effect your VPS or DS, and not other customers.
Be sure to include a valid "From:" header with your script generated email. Email must be sent "from" your domain, spoofing is not allowed.
I've all but stopped using dreamhost for email. I changed my primary email to a 3rd party several years ago. Yes it costs $4 USD/user to do that, however my overall monthly cost is still extremely low. I've expanded on that option in other posts in this forum, but it's a MS Exchange server which happens to work best with Outlook, and I can still use my dreamhost web server to send SMTP email via the 3rd party Exchange server.