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My personal book preference is an all-in-one core rulebook with the basics of playing the game, simple classes, basic DM advice, and a smattering of monsters. Kinda like a hardcover starter set but with full rules. So instead of the lame (LAME!) $boarded sets with enough content to psty for a long weekend, this is one purchase that has the entire game. Or at least 2-3 levels before needing a Monster Manual. 
And since the whole book is simple and options like (kinda like Basic D&D) it can be a little thinner making for a nice cheap price point. Making it very gift-able.
And it solves the flaw of D&D where you need three books to play. It makes answering the question "What do I need to start playing?" super simple: "Buy this one book. And if you like playing get the MM." 

The standard "starter set" could instead be an accessory kit with pogs and maps and character sheets and such, as a little bonus to help new players. So new players could avoid the annoying "drop $25 but you still need to pay the full cost later, so you end up paying more" problem.

Then the Player's Handbook would be a the PC rules plus. No reprinting of the core rules, as those are already covered. This book would be tonnes and tonnes of PC options and character modules. This can and should be a nice giant tome.
This does mean experienced players would need to carry two book from the start. However, this is ussually the case anyway after the accessories start dropping, and the Core Rulebook quickly becomes less necessary for *everyone* to bring as the rules are learned.

Then we get to the DMG. Like the PHB this should be big, unlike the dissapointing DMG1. Because the very basics of running were covered in the Core Rulebook, this can focus on advanced DMing, optional rules, house rules, and the like. This should read like the best of DMG 1 and 2 combined with advice on game design and world building.