I have a step I want to run every time Orchard starts. It will basically prime my app cache with some data structures from the db. Where is the proper place to set this up in an Orchard site? 

What do u mean by 'every time orchard starts'?

is it every new session?

Yeah, something similar to Globa.asax's Application_Start(), but for Orchard, where I'll have access to injected dependencies, NHibernate entities, etc. 

Did u see 'Orchard.WarmupStarter' module?  I think that would be helpful.