Thank you for the helpful replies here. I am looking to be as cross-plat compatible as possible, and my dev box is actually a Debian box, so components which strictly depend on Windows libraries are a no-go. The delphi-rest-client-api appears to depend on WinHTTP, and WinINET, or perhaps the README.md file wasn't updated after the Lazarus fork...
I will first give the RestRequest unit a shot, the one provided by Jurassic Pork, although I'd wish for as little external deps as possible, I'll check it out and see how it works.
In the end, I may end up rolling my own class using Leledumbo's suggestion of using fphttpclient+fpjson units, as this would make it more cross-plat, and would be more de-coupled from LCL components, so it has the benefit of working with both pure FPC(non-Lazarus) programs, and also working with Lazarus as well. I am also thinking of taking a look at the INet library, as I believe they also have a HTTPClient class which may work to communicate with REST as well.
As Leledumbo mentions, the only issue I may run into with rolling my own REST API client is dealing with authentication, but most endpoints just use a simple header, so that shouldn't be a big deal.