I'm looking to write a progressive desktop web app along with a progressive web app for mobile, given the variety of mobile browsers, what's the best sdk to use? I assume REST or HTML5, but github lists supported browsers, does that limit my ability to use those on mobile browsers for browser versions below those listed?
Selection of the SDK will depend on your app requirement. I would recommend you to go through Kinvey's documentation on following link:
Yes, Kinvey HTML5 SDK is compatible with the list of browsers mentioned on the Github link. It is recommended to use the browsers versions mentioned on the link.