My mother has a non profit organization, and it is hosted on Powweb. There has never been any downtime that I know of, but I have not heard very many good, or bad comments on them.
Best bet is to search, compare, search, compare, and search again! Make a small list of the things you MUST have, and another list of things you would LIKE to have. Then use that to compare hosts to your needs.
When you find a host that looks liek it might fit, send them an email about anything, then wait and see how long it takes to get a reply. Try their 1-800# if offered, and try their Live chat if offered also. Alot of hosts look good from the outside,but are AWEFULL once your in, and offer little or no support for their customers. Support should be a major factor when choosing a host.
Good luck! And DO NOT be suckered in by the $ 0.50/ month deals, as you will just end up doing your search ALL OVER AGAIN.