Hi Jamaican,
According to your description, my understanding is that you want to use Rest API to retrieve data from SharePoint Online.
Did you get Rest API 401 Unauthorized error?
If yes, this means rest api has no correct authorization to the site.
I suggest you can check the detailed web request using Fiddler to check the root cause of the issue.
Here are some detailed article about using Rest API for SharePoint Online:
Using the SharePoint CSOM and REST API with Office 365 API via Azure AD:
http://www.jeremythake.com/2014/06/using-the-sharepoint-csom-and-rest-api-with-office-365-api-via-azure-ad/
Calling O365 APIs from your Web API on behalf of a user:
http://blogs.msdn.com/b/kaevans/archive/2014/04/15/calling-o365-apis-from-your-web-api-on-behalf-of-a-user.aspx
Remote authentication in SharePoint Online:
http://allthatjs.com/2012/03/28/remote-authentication-in-sharepoint-online/
Best Regards
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