Getting started translating an existing API's schema / meta ?

Hello,

I've been reading about JSON-LD and Hydra recently, and wanted to use some
time during a "hack week" in our company to translate our existing schema /
meta info into one compatible with JSON-LD, but I'm not really sure where
to get started. Most of the examples I've seen have contexts that
ultimately resolve to schema.org definitions, and I don't know if that's
the right thing for us.

I'd love some tips on what I should do here.

I have a github repo with a summary of how our current API works here:
https://github.com/JogoShugh/JSON-LD-VersionOne/blob/master/README.md


Thanks for any input!
Josh