A few things I learned recently by gossiping with WMF quality assurance people:
We're deploying fresh code to the beta cluster ~50 times a day, or maybe even more often! https://gerrit.wikimedia.org/r/#/q/status:merged+project:%255Emediawiki.*+-o... shows merged code to MediaWiki core & extensions -- on every merge or every few minutes, we update the code on http://commons.wikimedia.beta.wmflabs.org/ and all the other beta cluster sites. So right now, beta is the best target for automated browser tests, but because of some configuration issues, http://test2.wikipedia.org/ is the best target for manual/exploratory testing.
When you're writing automated browser tests (good setup instructions: https://github.com/wikimedia/qa-browsertests ), "feature files" are a plain-English communication tool; step definitions are where the magic happens. So, in features/ , there's step_definitions/ with .rb files, each corresponding to a feature file. Look through those for some idea of the neat stuff we can do these days.
If you want ideas for useful automated browser tests to write, try looking at recently fixed bugs. That way we'll catch regressions.