I strongly endorse this, at least up to the sixth book, the last we’ve got. Among other virtues, it picks up on the Restitutor Reorum Romanorum concept, which is key to understanding why the Arthur stories captured imaginations and survived through 1500 years.
I went through an Arthur phase in high school and Arthur Rex was by far my favorite. Very, very readable yet tells the arthur legends (and associated legends) in great detail. It’s our of print now but it’s easy to get a used copy.
Aside from many already mentioned, I enjoyed the first three books of the Pendragon Cycle when I read them in High School, back when it was just the Pendragon Trilogy. I can’t vouch for the subsequent books as I haven’t read them.
Only thing I can add is that Bullfinch’s Mythology touches on many of the tales.
Seconded. Start there and then expand into the contemporary stuff. When I was 16 and (we were on our family summer vacation in a motor home going from SoCal to British Columbia/Alberta and then back down the Rockies and back to SoCal - 3 weeks total), I spent half my time with my head in Le Morte D’ Arthur. The old english was rough to understand at first, but when I started understanding it as I kept reading, I felt like I was witnessing Malory’s writings firsthand.
And there was a WHOLE lot of smiting going on…
Some of his short stories are wonderful - *‘The Black Rabbit’ * (A boy’s encounter with Pan), *‘Soft Voices at Passenham’ * (A genuinely scary ghost story) and *‘The Point of Thirty Mile’ * (A foxhunt catches a werewolf) - are some of my favourites.
Got some collection titles, please? 
Already noted by others above, but I’ll add my votes for:
Best Arthurian movie: Excalibur, dir. by John Boorman - Visually stunning. Great use of Wagner and Orff in the soundtrack. A nice blend of mysticism and realism. You’ll never see a better Merlin, and there are very early appearances by Gabriel Byrne, Patrick Stewart and Liam Neeson. =Sigh= If only they had more money to do the final battle scenes right (but that’s a small quibble).
Best Arthurian book: Arthur Rex, by Thomas Berger - By turns thrilling, funny, sexy and deeply moving. I first read this in high school, and come back to it again and again. Simply outstanding.
The three stories I mentionded can all be found in **‘Gone to Ground’ ** - detals here:
http://www2.netdoor.com/~moulder/thwhite/gtg_b.html
Sadly, long out of print. The good news is that they (and several more of his best stories) can be found in ‘The Maharajah and Other Stories’ - a sort of ‘best of…’ compilation which can still be found fairly easily - at least in Europe. I’m not sure about The States.