The story makes more sense if you consider it and the 2nd movie just two halves of the same thing.
Sparrow was killed and became a slave to Davey Jones, he just didn't have enough time to go full zombie yet, and the contract was cancelled when Jones died.
The voodoo chick was Davey Jones' love. She was the personification of the sea, and Davey loved her so much that he chose the job of being ferryman to those who die at sea, because it meant he could be with her for eternity. It's pretty much the same story as Thanos trying to impress Death.
But, remember, Davey Jones could only spend 1 day on land every 10 years, and the chick started spurning him, missing out on the once-a-decade rendezvous. That made Davey go insane and cursed her into human form.
Barbarossa was brought back cause he was the only one to stand a chance against whoever they were up in the 2nd movie. I think. I forgot most of the 2nd movie, admittedly.
The 2nd movie was the one that had everything disjointed, and the 3rd movie did okay to bring all those elements back. However, the 2nd movie set up where everyone stood in the 3rd one, so the 3rd movie makes little sense without knowing all of that. If anything, the third movie made up for all with the visuals. The ship fight in the whirlpool was so fucking beautiful, and so was the navy guy getting double broadsided and his ship blowing to splinters step by step in slow motion. Or the whole Jack Sparrow going insane scene. Or the execution scene one minute into the movie.
The first movie had the best focus, I agree. But it was also the most Disney joke-a-round, and it had zombie skeleton pirates, ARRR! The other two tried being more serious and more epic in scale but the script wasn't tight enough, so people couldn't understand what the fuck was going on.