I don't mind some shout outs in the form of cameos and easter eggs to the EU, but thats it.
We already have hints from over the years that pointed at Lucas wanting a third trilogy to be existential, dealing with metaphysical philosophy and internal struggle.
Luke Skywalker as the subject of that struggle would be perfect. He doesn't want to become like his father, but he doesn't want to make the mistakes in his new Jedi order that the old one did before the fall of the Republic. He ends up trying to walk a fine line with the Force making the new order somewhat grey, rather than black or white. At the same time he becomes aware of the galaxy's future and is faced with a moral and ethical problem similar to Hari Seldon of Foundation and Paul Atreides of Dune, where he knows a collapse of galactic civilization followed by an age of barbarism and darkness is coming.
When faced with an external threat to the new Republic, Luke and the new Jedi order are faced with tough moral choices in how to protect the Republic. I wouldn't use an enemy from the novels, no Sith, Imperial Remnant or Vong. I would use something different, an enemy that can perform kamikaze attacks without warning, hides among and uses the innocent to complete its objectives. It would be a protean enemy that could take control of others minds or even mimic others, with the ability to cloak themselves, maybe even use somekind of phasing or teleporting technology. I would keep their nature and origins in the dark at least till the end of the second film.
The end of the second film would reveal their origins directly involved Luke Skywalker, with the entities as a monstrous force he helped create or release but lost control of, probably in the course of trying to save civilization. Luke is then faced with the dilemma of falling further into the Dark Side to fight and destroy this enemy, while at the same time the new Jedi order splinters into factions and the Republic experiences disorder, unrest and martial law.
The last film in the trilogy would deal with Luke's sacrifice as he falls to the Dark Side to save the Jedi and the Republic from collapse, preventing a new dark age from falling upon the galaxy. Other ideas thrown into it could be the destruction of Coruscant, Luke's transcension to becoming a force being of balanced light and dark, the union of the Jedi and the Sith into a new order, galactic cycles of destruction, and the revelation of the precursor civilization known as the Architects.