Either will work, but you need to be careful with whichever you choose because some of your fish will be sensitive to either the salt or the medication. You should start with 1/2 of the recommended dose, and slowly increase the amount watching for signs of stress in your fish. It also helps to raise the temperature (a few degrees each hour so the fish can adjust) while treating for ich, but with the corys, you may need to watch them for heat stress, because some of these need cooler temperatures than others. It would be good to have the temperature up to around 86o if they will tolerate that level, but any increase will make treatment be more effective sooner.
With both treatments, it will take around 14 days, or at least 3-5 days after you no longer see spots on the fish. Stopping treatment any sooner will put your fish at risk of reinfection, because it's not until the parasites are off the fish (where they're enclosed by a protective cyst) and in the water that the treatment begins to kill them.
Since you have such a mix of fish, if you have a spare tank, you might want to consider treating the sensitive fish (corys, tetras, and pictus) separately from the ones that are more tolerant of salt and medications.
The barbel of you pictus was probably injured by getting caught in th filter intake or by bumping against an object in the tank - when fish have ich, the often scrathc against objects (called flashing) to "scratch" their bodies to try and remove the irritation from the parasites.