Unless things have changed, The Salt above the 60 bridge is illegal to run so no permits needed. People actually run the white and the black above the confluence that forms the Salt but there is no way of knowing when that will run. It is also at least an overnight self support.
What most people call the upper Salt starts at the hwy 60 bridge. There is a day run that requires an Apache day use permit that was $10 a head per day as of four years ago. Good play above 800, Great play above 1000 and mind blowing above 2000. Especially right at the end. You can actually drive to the take out and play and hike back to your car if that is your game. If over 2000 it is worth the effort of paddling down to Ledges and hiking back up. To run the rest of the wilderness section you need a forest service permit which is lottery based. You can get cancellations as long as you are not trying to go on a weekend or during spring break. I would recommend a four day trip though some commercial groups do it in as little as two days with car support. At that time of year many of the rafting companies will help you with shuttle. Which is about an hour and a half one way. This is one of my favorite wilderness trips in the west and I have been on it down to 400cfs and as high as 7000. I have no real beta about section above hwy 60 except it is class 5 and though not the gnarl it is an undertaking that requires so knowledge and scheming.
friend of the fork, knife, and spoon