That can be a tough decision. It greatly depends on what the application needs to do (or have access to) on the phone's hardware and also availability if the user is not in cell/wifi range. If internet access is not a concern as it is a core requirement then a Turbo Native approach could be the easiest path. This way you wouldn't need to maintain the API as well as a full fledge mobile interface as the ActionViews would be used. Alternatively, if there aren't many requirements for the hardware of the device (no need for NFC, camera, GPS, etc), you may be able to get away with a PWA. 

Honestly, I would explore these two routes first before jumping to a React Native approach.