"Cheap", "reliable" ,"important", "time-sensitive", " alot of money", etc. are all terms with "relative" meaning; these terms mean different things to different people.
I think you took kchrist's statement the wrong way. The measure of how "important" emails are to you should have a relationship to the level of service, redundancy, hardening, etc. you are willing, or able, to pay for to keep that fucntion sufficiently "reliable".
Dreamhost is primarily a webhosting service provider; I appreciate the added benefit of using their email servers, but my ISP's email servers are also available for me to use, and I can always go to a dedicated email provider if I find Dreamhost's mail service insufficiently "reliable". Believe me when I tell you that, in "the real world", you'll be hard-pressed to find mission-critical redundancy and hardening for your email services for $20.00 a month.
I'm sensitive to the fact that for non-profits cash money is hard to come by and you hate to part with it for infrastructure, hoping to pass more of that cash onto your mission. It remains, however, that you need to take some responsibility for your procurement decisions; if you go the "cheap" route and find your email is occasionally unaccessible via a webmail interface (there is still POP which, in many cases, works fine even if webmail is "borked"), delayed (very rarely is email lost; it is usually "spooled" until the services are repaired), or in some other way more problematic than it would have been if you sent more money for a more robust email facility, you should accept that you made that decision.
I believe Dreamhost fairly represents the services they attempt to provide. Their TOS are clear about the nature of "shared hosting", and these forums, as well as other internet resources are readily available to help you decide whether or not Dreamhost is a "good deal" for you.
Since 1998, Dreamhost has been a very good deal for me. That does not mean that I am not frustrated when problems arise (I've been very frustrated with some of the issues of late), but my perspective over time is that Dreamhost has been, and continues to be, an excellent value; you'll get more for your "$20" here than any other place I know of (when the total package is considered).
I believe "trying to stop childhood cancers!" is a great endeavor, and I try to help charities with noble goals as much as I can (I always have one "pro bono" web development project on my desk along with the paying ones ).
Post a link to your organization's website, from which I can determine your organization's "section 501(c)(3)" status, and I'll donate a new keyboard (that doesn't have a "b" stuck in "CAPS" mode) you your cause*.
* Offer restricted to standard "IM PC Compatible" style keyboard suitable for use with Linux or Wind*ws OS desktop systems. Sorry, I can't afford a new laptop or Mac keyboard.