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This really depends on your situation. If you are writing a reusable app, then you probably want both unit tests and a sample project to run integration tests against.

For testing a basic website, you'll probably want to test any custom managers or model methods, and your views. A good guide to getting started is here: http://toastdriven.com/blog/2011/apr/10/guide-to-testing-in-...

For full-stack tests, you can use something like Splinter (http://splinter.cobrateam.info/).