Most Platform-as-a-service vendors work on instances. That's one of the benefits over traditional hosting (since you can scale on demand)
I wouldn't rule out Azure completely. An extra small instance costs around £30 a month and the Windows Azure Accelerator for Web Roles allows you to run multiple web sites on one instance.
I've never used AppHarbour but considering they'll give you a single instance free, I'd say that was a cheap startup. They don't have any requirement that you use CI but I do believe you deploy using Git or Mercurial so the deployment experience isn't quite as "nice" as Azure (not that Azure's is perfect by any means).
Typically however, "fast, reliable and cheap" won't come together.