How to test a Web Application completely?

I have a Web Application in Vaadin. I would like to perform some testing. But I'm very new to testing so I do not have an idea about all the kinds of testing that can be done on this application.

For now, I only tried some automated GUI testing using some tools like Selenium IDE, RobotFramework, Ranorex and Rapise. However, Selenium and Robotframework is not completely compatible with Vaadin and I checked TestBench but it the latest version of TestBench, they removed the record and play option. The problem Ranorex and Rapise is that they are licensed products. I prefer using an open source solution for now.

Question is:

1. What is/are some tool(s) which can easily help me with record & play GUI testing my Vaadin Web Application?
2. What are some other kinds of testing and the respective tools I could use for testing a Web Application other than record/play GUI tests?

Either one of both answers would be good! Asking for advice as a novice, hope to receive some answers from you experts!

P.S. - I would prefer to use some easy to learn and use testing tool, especially some gui record and play or some tool with less coding (which means I do not prefer tools where I'd have to hard code the tests like in JUnit)

Thanks!