My favourite ‘complete’ but ‘minimal’ version of D&D remains the Moldvay/Cook edition of the B/X (Basic + Expert) rules...
But the 5e version of ‘Basic D&D’ is probably now my second favourite version. I’m itching to use them to run a 5e version of The Keep on the Borderlands or The Lost City. If only a print version were available!
In addition to incorporating errata and the like, the new PDF includes a number of (surprisingly evocative) sketches by Richard Whitters. Some samples: