Rails: how to test a whole scenario

I have a small project where I need to write some testing for couple of functions. But the tests need to be done for a complete scenario. For example, First create a customer and save it in the database, then create the type of work and its details and save it, then test if the customer fulfill certain criterias? There is another table where these criterias are saved.

Now I have to create several variations of customer work details and check against the saved criterias from criteria table.

My question is, how to test this whole scenario. What type of test should I use funtional test, integration test or what? I don't need configuration details. Just idea which test I should use and how to proceed?