Before you start diving in nearly five hundred years of literature, you may want to revisit your own Arthurian tradition. Can you find the book that introduced you to King Arthur when you were a child (I can: ISBN 9782010029707)? Have you recently seen a movie or TV series with King Arthur? What did you like best about it? Take a few notes concerning the major characters in it (Arthur, Gawain, Guinevere, Merlin, Lancelot, etc.), as well as your impressions. When you emerge back from an extended stay in the middle ages, you will see these works in a completely different light, and you should get thereby a better understanding both of them and of your contemporary world.
If being a fan of medieval High Fantasy (J.R.R. Tolkien, George R. R. Martin, etc.) drove you to Arthurian literature, you’re in for an interesting shock: fantasy medieval is nothing like real medieval literature. But you’ll also better appreciate the innumerable borrowings.
Once you’ve completed this little self-assessment, it’s time to decide if you want to read in a roughly chronological order (to see the process of appropriation and rewriting) or in an anti-chronological order (to appreciate a growing historical distance as you reach far back into the roots of more recent works).
We’re used to literature surveys being chronological because we understand historical things in terms of birth, growth, and decline, but if you’re reading things backwards, you may better appreciate how these texts came all the way down to us. The 19th and early 20th century adaptations will be of crucial importance here, since it’s often through these keyholes that further explorations of the past have proceeded.
Another good reason to read backwards is when a late medieval author like Sir Thomas Malory is your starting point: Malory is one of the most often taught Arthurian authors in English departments, but he in fact boiled down together centuries of Arthurian tradition. The demands of scholarship in the sources of Malory have justified the unearthing and translation of a myriad of secondary works, and you may better appreciate them after you’ve read Malory.
My own survey was initially anti-chronological, since my point of reference was Malory, but I drifted very quickly towards Welsh works such as the Mabinogion by way of reading Tolkien, so I ended up reading things in a roughly chronological manner.