You are right - most recruiters and directors/VPs don't know much about Sinatra, so use them for learning, for your own projects or for other projects once you get a contract or FT job. However, Rails is what people look for and will use for questions on tech screens and likely have in place already for most projects.
I have noticed that most constructs in Rails require little more than conditions, loops, and a basic knowledge of Ruby itself to get moving on most Rails projects, so it might not be too difficult to start out with Rails. However, a deeper understanding of Ruby will allow you to better read, understand, and extend the code or write your own that accomplishes more with less than if you stick to the language basics. However, your plan for starting with Sinatra isn't a bad idea, at least to get a good grasp on Ruby first (and to remove too many moving parts at once as you learn).
FYI, Sinatra is gaining some ground, but isn't nearly as popular as Ruby:
Rails:
Sinatra:
James