I started to self study Plato but I am not sure how to arrange my knowledge. In general philosophy books, Plato's philosophy is separated by subject matter (metaphysics, language, ethics), but this can be difficult to sort out when I'm reading his dialogues. Basically, should I be sorting my knowledge by each dialogue or by subject matter? Thanks.
In my opinion, the best way to self study Plato could be:
To start with a short Plato biography: When did he live, what are the characteristics of his time? Why did he travel to South Italy, how is his relation to Sokrates and the school of Pythagoras? How is the relation between Aristotle and Plato? I would focus on the facts, less on the comments referring to certain philosophical topics.
Secondly I would read a choice of Plato’s early dialogues: Apology, Kriton, Ion, Euthypron.
When arriving at this point, you probably have consulted some secondary literature and found out, what type of secondary literature and which scholars answer your questions best. On the academic level I can now recommend (see the comment of Mauro):
Benson, Hugh H. (Ed.): A Companion to Plato. Chichester, West Sussex 2009
Fine, Gail (Ed.): The Oxford Handbook of Plato. Oxford 2011
You may go on reading some dialogues from Plato’s middle period: Book 1 of Politeia, Menon, Phaidon, Symposion. In addition: The parable of the cave and the parable of the sun from Politeia, Book 7 and 6.
Eventually, from the late period you could try, e.g. Theaitetos, Parmenides, Timaios.
The whole enterprise probably takes one year. But it is worth this time. Because afterwards you are able to critize Plato on the grounded level that you have read his texts before :-)
Added. Politeia (Greek) = The Republic (English)