Server based auth flow and api calls -- NO WEB BROWSER in this flow.

I'm trying to build a server based integration between my cc account and a node server (our backend).   Use case is updating specific contacts with additional info such as a unique short-code to enable access to our iOS app.  

• Elsewhere: Typically this would happen by various means, such as an API KEY in the header or  getting an auth token,  and then including the token in api calls. 
• How do I make API calls to CC?    The OAUTH workflow won't work as the calls are coming from a server that can't use a web browser flow.    

I'm a new customer, and the sole reason we chose CC was api capability.