Max Hasting's Overlord is a perfectly good general history and benefits from being very readable, Cornelius Ryan and Stephen Ambrose are very good on individual and small unit stories; Normandy '44 by James Holland is an excellent narrative of not only D-Day but the whole Normandy campaign, Anthony Beevor's book is very good.
John Keegan is a world renowned historian and Six Armies in Normandy is a fine book, but he is a bit of the declinist view of British history which you may or may not subscribe to; Carlo D'este meanwhile has a not particularly balanced point of view best summarised as "the Brits were useless, Monty was rubbish, the US won the war on their own etc etc..." which may cause the more anglophile reader to throw his books across the room.