Your recommendations and suggestions here are absolutely terrific. I took courses in ancient lit and Greek lit, but Modern was my period, though I loved the ancient stuff and have a decent collection in my library. Maybe suggesting a good anthology would be a better starting point for someone new to ancient theater?

However, and I'm sure this is different in Europe, and I'm not as familiar with college theater, but I disagree that the plays you listed are "fairly regularly performed". I also think that most people in the US don't live anywhere near a city that would ever perform ancient theater more than once in their lifetimes. I agree that seeing a performance would be the best way to appreciate them, but I don't think that includes a bad college adaptation. I know that these plays are regularly performed in the traditional way in Greece. You can definitely find videos of these performances online. But I think to better appreciate a live performance, even a contemporary adaptation, it would be better to study the literature and history first.