Best way of testing an application which you only know its functionality

I have received a software application without test which I'm going to refactor. The client has shown me how the app it's suppose to work and I have written down all the steps. The application is quite a mess: names are not related with the actual propose of the code, there is unused functionality and a long etc. I'm going to refactor it completely but before doing that I wanted to create some tests so don't break the whole system. I'm going to change the steps in which objects are created because I think it's not user friendly.

I'm wondering what would be the best way of testing in such a case. Since I only know the effect of the action of the users, I think feature tests or integration tests would be the best way to go because it's the information I have. On the other hand, as I'm going to change the UI, I think I would need to tests against the database, and that's not what feature tests are suppose to do.

Would it be a good idea to reproduce the scenarios on a browser and then check that the database state it's as I expected?

Thanks in advance