Hi Kasper, it comes down to the commentary resources which are easily available to you. The 3 main tragedians are Aeschylus, Sophocles and Euripides. Pharr says that (page vi) "Euripides furnishes the easiest reading" and Aristotle says that he's the "most tragic" of the 3: if you can get a good commentary (or 2 commentaries, because often one supplements an earlier one) you could make a good attempt. I've read the first few pages of the Medea but I don't find it easier than the other authors: maybe when you get further in, into the main dialogue, it's easier.
I personally prefer Sophocles, because you can get the Jebb commentaries (which are really good) on Perseus and I like the way he writes. I've only read parts though: I'm just a beginner as well. Sophocles was described as most Homeric: "Homer is epic Sophocles, and Sophocles is tragic Homer" or something like that from Diogenes Laertius.
If you want to read Aeschylus, the one to read is Prometheus Unbound: a commentary says it's far easier than other Aeschylus plays, and might have been written by someone else. And there's a commentary here on textkit, although the comments are pitched at an intermediate-advanced level. If you got another commentary for beginners, you could have a good attempt at this one.
On the other hand, the only surviving trilogy is by Aeschylus, the Orestea, and that's something I really want to read in Greek as a long-term goal: tragedies were written and meant to be understood as parts of a trilogy. The start of the first play in this only existing trilogy, the Agamemnon play, is really good and not too hard, a sentinel on the roof watching the stars.
In terms of style differences, Aristotle describes Aeschylus' plays as 'simple' in plot: the causes of the downfall happened before the play begins; what you see is the unavoidable fated downfall. In Sophocles there's a bit more choice involved; the downfall has a human as well as fated part... Euripides likes to show human wickedness
As another option, something else to think about, I have a good little commentary of Aristophanes' Birds: all the non-iambic bits, and the hard iambic bits, have been cut out, and it's really funny, Aristophanes is hilarious I've discovered. There's lots of resolution in Aristophanes, almost every line: the commentator says that, if he hasn't got resolution in a line, chances are he's pretending to write in snooty tragic style
So I think it'll come down to whatever good commentary resources you can get: for iambics you need them. I've talked about a few authors here so that you can choose which one you want to go with. If you find it too hard, you won't have lost anything making an attempt, and you'll have an idea of the poetry style so appreciated by the Greeks
