Whenever you feel ready to test your React Native and Redux progress, then head straight to Barton Hammond's Snowflake repository.
It demonstrates a lot of concepts around React Native: a single base for both iOS and Android Apps, a great Redux starter project a Login flow backed up by Parse, and more.

snowflake on GitHub

A React-Native starter mobile app for iOS and Android with a single code base. Using Redux and Immutable, the state of the application is fully testable with Jest. Snowflake supports Hot Reloading of its state. Snowflake uses CI with Bitrise.io and has extensive docs and 45+ min of video demonstating implementation.