Ask HN: Creating a REST Api to power client apps?

[cookerware]

I'm looking for any bit of advice on what it will take to create a REST API for a company that is looking to release web,mobile applications based on the API?

What tools would you use for development, deployment? Am I better off using a SaaS service that does this like apiary.io? Ideally, we want to own the whole REST api stack, what would be some great tools?

In terms of deployment, is EC2 generally the way to go?

In general, is creating a REST API hard thing compared to building an web app? There's documentation that must go with it as well.

How do I pitch this to my employer, that instead of building separate applications tied to their own databases, we create a central API that the client facing applications (Android, iOS, single page app) can consume. How can I estimate how much this will cost to make and explain that API first approach would offer more value? How do I explain that this in the long run is the ideal place to be without overloading them with technical jargon like "decoupling services and consumers" etc.