How should I test a java rest api?

I want to test my rest api, but I'm little confused how to it. Is not about which lib to use, but what should I test.

My application is basically about cruds and reports. Some specific cruds populate another tables based in the state of the entity submited.

If I want to test those behaviours, should I test the service/repository layers directly or make requests to my endpoints?

P.S: My application will be consumed by a SPA. So probably I need to test the requests of that application too, right?