How to write integration tests correctly?

Question

Software testing

Let's say that my service interacts with the database. I'm aware of three options for how to test this interaction:

• Mock in which I will keep track of which methods I call
  
• Some kind of embedded fake that I can interact with as usual and check what happens in it
  
• Raise the container with the base and walk into it
  

In what cases, which option should be preferred?