So in mine, Anakin is basically a minor character, a maguffin in the prequels, and the narrative focus is more on Obi Wan (the movies we got couldn't seem to decide whether they were about Anakin or Obi Wan, but I always thought they should really be Obi Wan's story). Anakin's fall comes a bit earlier, maybe in episode 2, as I felt it was rushed and forced in episode 3. I'd still find a way to include Dooku, because Christopher Lee rocked. And maybe Qui Gon too. However, in my version, Dooku is more like a Saw Guerrera type of figure. When he tells Obi Wan he's actually fighting for the good, he isn't bullshitting like he is in the movie we got. This makes his defeat at the hands of Anakin all the more tragic, as his initital portrayal as a villain and terrorist would have been a result of propaganda spread by agents of Palpatine, since he would need a big bad to justify his need to escalate the war and consolidate his power. Episode 2 would take place right in the thick of the clone wars, rather than being about the lead up to the war (the lead up would be seen in episode 1). And what the hell, I'd still include Darth Maul, only expand his role quite a bit.
I'd also have the jedi portrayed as a less centralized order. It would be disorganized, with several different branches following distinct philosophies. There would be some dark/grey jedi and there would be some branches opposed to the war and resisting any involvement.