This might be strange, but when I choose a service I tend to look who's who behind that.
To me it is important as I know any provider could easily access my containers, leak my personal Information, CC, etc., therefore I appreciate certain qualities from my providers.
Trust - Not simply blind trust of a desert dweller to his leader, but more to how they run their services as well as handling and protecting my data.
Helpfulness - Most of my services are unsupported. Some providers simply ignore my tickets, some who also offer managed services reply and explain that my request is not included in my package, some are willing to help then or at least they point me to the right direction i.e. "O.K. we'll help you this once, but please read this tutorial in our Knowledge Base or at this url" or "Your service is not supported, but you can read tutorials in our Knowledge Base or at this url".
Openness - some providers hide incident that happened to their gear or network, some openly inform customers of what happened and provide some directives of what customer should do in such situation, and keep the customers up to date.
Common Sense - related to TOS/AUP & incident. i.e. some ignorant customers uses unsafe application, got hacked and sending DDoS attak or unsolicited email. Some providers directly terminate the service, but some are willing to help the customer pointing them into the right direction and mark the specific customer to know whether the incident is on purpose or simply out of customer ignorance. At this point providers have full right to probe what is in customer's container using automated means or manually.