Well first off I would go back to the OUT and make a bunch of notes on any allusions the characters make to significant events in the past, or anything they establish about the way things were. That would be the canon I would work with.
A New Hope follows a revolution. Similarly to 1984, very few people remember what life was like prior to the revolution and only a handful of the ones who do talk about it. To make it convincing, one would probably have to look at a seizure of power in recent history - such as the ones that took place in Russia, Germany or France, and base the story on a combination of those. Palpatine's rise to power in the PT as we know it is clearly based on Adolf Hitler's. However, I think given the context of A New Hope (in a deleted scene, Biggs and Luke talk about how the Empire is beginning to 'nationalise commerce in the central systems', implying that Palpatine's rule is of a Marxist nature), Palpatine's rise to power should be more in the vein of Lenin's - i.e. one executed through force.
Now that the political background is established, we of course need a character story to take the fore. A New Hope has often been referred to as a 'road movie in space', and I believe another cinematic archetype - the 'buddy movie' - would be perfect for Episode I. The 'buddies' in this case would of course be Obi-Wan Kenobi and Anakin Skywalker. The first meeting of these characters would be important, and they would have to build a strong friendship throughout Episode I, just as Luke and Han do in A New Hope. One could perhaps cast Anakin as an adventurer, living a life of thrills and excess with his brother Owen. Then he and Obi-Wan are thrown together in unlikely circumstances and forced to work towards a problem despite their differences. At first they dislike each other, but at the conclusion of Episode I Anakin comes to respect his new mentor and pledges to become a Jedi Knight, following Kenobi on a 'idealistic crusade' at the disapproval of his brother.
Episode II sees the Jedi drawn into the Clone Wars*, with Obi-Wan unable to complete Anakin's Jedi training. Anakin is regarded as a maverick by his peers; he has a far less rigid morality than the average Jedi, and will often use questionable methods in order to do what he believes is right. Most disagreeably for his fellow Jedi, he retains his lifestyle as a party animal, and surrounds himself with vices whenever not carrying out his duties. Obi-Wan on the other hand has a strict devotion to the Jedi creed, and is seen as the Jedi order's poster boy by many. The Republic is at this point clearly losing the Clone Wars, with even the core systems becoming battlegrounds. The climax of the film would see Anakin doing battle with an evil Jedi for the first time, and clearly drawing on the dark side of the force, but ultimately being defeated. Following this he is taken hostage by the Republic's enemies and held captive.
Episode III poses a major problem, as it will inevitably be darker in tone than the other two, but it also needs a certain amount of denouement. The beginning of the movie sees Anakin and Obi-Wan reunited to take part in a battle that will decide the fate of the Republic. Most of the film is based around the lead up and actual fighting of this battle. It is made clear that our heroes are getting old - Obi-Wan is beginning to look wizened and pessimistic, while Anakin's life of excess has clearly taken its toll on him. The two have also become bitter as a result of the perpetual war, causing disagreements between them frequently. Ultimately, Palpatine's forces crush the remaining forces of the Republic and he takes power. At this point, an ultimatum is offered to the Jedi and the Republic at large: serve the new Galactic Empire, or face persecution and death. Anakin, ever the maverick, sees the new Empire as a positive development; he is keen to see the end of war, and for some order to be restored. Palpatine realises the young man's potential at this point and takes him on as his apprentice. Obi-Wan on the other hand stays true to the Old Republic, and the two do battle. Obi-Wan wins, and Anakin is horrifically disfigured. In disgrace, he locks himself into a suit of armour, and abandons his former title in favour of one that suits his now patriarchal role in the Empire - Darth Vader.
The conclusion of the trilogy would see the remaining Jedi forced into exile due to the persecution of the Empire, with Obi-Wan returning to his home world of Tatooine where he learns that Anakin had fathered two illegitimate children. I'm sure you can all guess where this is going, so I won't bother explaining any more.
* The Clone Wars would see the Republic's combined military forces going against Palpatine's revolutionary force, made up of clones.
Obviously Obi-Wan, Anakin and Palpatine are not the only characters that would be present, and the story needs a lot of fleshing out, but you get the idea. Also a strong villain would need to be present throughout, below Palpatine, though not necessarily his apprentice. Perhaps the commander of the Clone army could be a former Jedi, but I haven't given it that much thought.