If you want to avoid dealing with infrastructure directly, you definitely want one of the "full service" specialist Rails hosting providers, because they'll deal with all the headaches on your behalf. Trying to go with a general-purpose hosting provider (or, even worse, a general-purpose infrastructure provider like Amazone) will end up with you doing most of the work, because they don't have the time or margins to deal with getting up to speed on all the various technologies that you'll be using.
"We don't want anything too expensive" means that you're probably pretty screwed, and you will end up doing most of the work. For instance, Engine Yard are very good at what they do, and will save you massive amounts of time and hassle, but they charge a small fortune for their traditional systems and support. EY Solo is a cheaper option, but lacks the support that IMHO is crucial to ensuring that you have a "fire and forget" hosting platform.
Heroku have some interesting ideas I agree with, but due to the way they do their infrastructure, unless your set of technologies dovetails with what they support, you won't get very far there.
Ultimately, I think you're looking for something that doesn't (and can't possibly) exist. Managing a hosting setup isn't easy, and it isn't cheap, and either you pay that cost in cash, or in staff time (or, far worse, in unreliability and customer dissatisfaction).