Recall the concepts of the test pyramid

The test pyramid has been designed to identify and recommend the placeholders for automation activities at the different layers of testing. Following is the diagram of the recommended test pyramid

The size of section in the above triangle shows the amount of test automation you should be doing during your sprints. Unit tests are mainly written by the developers. They can use framework like Junit to write unit tests. The objective of unit tests is to test small units of the code. As the unit tests are executed at the code level, these test are very fast . Because they are fast, the feedback process becomes fast and fast feedback is the fundamental principle of any agile delivery.
Service layer test automation is based on testing the webservices,messaging queues, databases etc.
In these tests you can test the status of the API by configuring tests to send various requests and then validating the responses using assertions. You can use open source tools like Codeception Rest/SOAP Module or SOAPui to do web services testing.
In one of the projects I was working on , we had a complicated task of validating that the data coming from mule integration service is the same as the data in the legacy system. Without automation you would actually spend hours in validating the xml response with the data in the database. Using free tools like SOAPui and groovy scripts our team automated their comparison. This reduced the test execution time to seconds.
UI tests are the slowest tests in the automation stack. There are plenty of tools both paid and free that are available in the market. It is normally recommended too use open source look like selenium if your developer have not added the proper ids against UI fields, you can expect a brittle framework even after spending a lot of automation effort. As an testers you will have to negotiate with your development team to either add ids to the product fields or just add unique automation ids just for automation.
For one of our clients who had a financial service product we justified an extra development effort to the senior leadership team .After adding the object IDs against fields the automation framework become really stable
I also had an opportunity to work on a famous insurance product called "Guidewire".Guidewire is currently being used by top insurance companies worldwide.It is a very solid product in terms of object IDs. Each field has a proper ID using which you can identify that field and do any operation on it e.g clicks, fill fields, select values from a dropdown etc .
Following is the basic architecture diagram of a UI automation based framework