Try the petstore - it's a common API used in examples. I used it when working with JMeter and it's a useful API to practice with.
You can do all sorts of different things there.
The answer depends on many other factors including the infrastructure.
Even POST requests can create unwanted changes in production DB so GET is mostly the only safe method, investigate if this is the case for your product.
Do you have a staging server where you do rest of the use cases (if you plan to use only POST and GET in production)
What is your team ...
My personal take:
At a high level
Test the API Endpoints, Status Codes and Data with Smoke, Happy and Sad Tests
At a detailed level one needs to ask the following questions.
The answers will guide what and how to test.
What documentation exists ?
What functionality it provide ?
Does it support concurrency ?
What are the API endpoints ?
Is the API internal ...
Restful-Booker is purpose made for learning to test an API. You can either use the online version, or you can check out the repo and run it locally if you prefer.
I think it's a pretty useful site to practice with, and it does seem to be actively maintained - the author has written a couple of courses on API testing which are pretty useful (linked from the ...
This and this GitHub repositories provide a curated list of service projects, many open source, and buildable by running a couple of Docker commands.
You may also want to visit this site.
As an example of a simple API from a "real site" is Trello.
I've written a blog post showing a CRUD cycle in it for Postman. Nonetheless, it's direct to ...