Hangouts application not always suggesting my contacts when searching
For those asking for a clearer, illustrated answer:


Click on the (+) New conversation
On the right hand of the search box, click on the really-nonobviously-a-modality-switch phone icon:


Search will now be limited to your Google contacts. 


Presumably some designer made a bizarre choice to use a phone call icon to represent the phone address book.

Note:  When texting rather than calling, be careful not to click on the contact name rather than the small SMS icon on the far right as this will immediately initiate a phone call.  (credit to Dan Csharpster)