I cut my teeth on reloading for the .357 30+ years ago and started with Hercules 2400 powder. Works better in barrels over 4", and have used several other powders with equal success. There are many factors to consider, gun type, barrel length, type of bullet, and what you expect from your reloads. H110 has given me the most velocity from the .357, but 4227, 2400, and Lil gun also do well. I have 2 different loads I use in my .357 handguns, a hard cast 158gr plinking load with AA5 or Unique, and a high velocity 100yard loads with XTP bullets with H110 or 4227 powder out of 6-8" guns. Let us know what you're wanting these reloads for, and what gun you are shooting them out of, and we can give you some better guesses on what will work best for you.
As Far as the brass, never heard of the Independence brand. Surely they'll give you a few loadings before any problems arise, if the primers seat snug and there's no splits or cracks in the case walls, load em up, wear them out, and buy some Starline after they're gone.