Whatever you want. Just pick some small attribute that you expect to observe.
I'd personally start with failure modes as they are the most important and interesting code you will write. Hell, you can likely not even bother testing the so-called "happy path" because, really, who cares what happens during success? Failure is where you want users and future readers to have the most documentation to ensure that when things go wrong the metaphorical bridge doesn't come crashing down into the river but rather remains in a repairable state.
If it's a REST endpoint that aggregates data from multiple external services, you probably want to see a "retry after" response sent to the client if any of those external services are temporarily unavailable. So write a test that asserts that, then write code that does it. This is also a nice first case as you can detect an unavailable external service quite early in your pipeline, requiring very little of the implementation to see the test pass.
No need for religion. If documenting your code later works for you, go for it. Nobody cares. Tests won't be driving your development, so it won't be TDD, but it'll be something and that may be enough. However, in reality most people simply don't have the wherewithal to plan for things like being able to test unavailable remote services if they don't have a test case in front of them forcing them to and won't bother when it is too hard to add later, so there is something to be said about the TDD approach as a general rule, deviating only after you fully understand the tradeoffs.