For the wires, use black for ground and red or white for anything carrying a signal, which is basically everything else. Use the braided wire, which is basically a coax, for the output to the jack. Strip off some of the plastic coating at the end and unravel the braiding to expose the underlying coated wire. That is your hot. Strip that and solder it in place. Twist the ends of the unraveled braiding and use that as your ground.
Regarding soldering, here are a couple of tips. One, make sure to "tin" the iron. By that, I mean to put some solder on it once it gets to temperature, then wipe it against a wet sponge. While it is on and not being used, repeat that when the tip starts looking dull.
Two, when soldering, apply the tip of the iron to the two items to be soldered and heat them, then add the tip of the solder to the mix. Otherwise, you'll get a "cold joint." For the grounding on the back of the pots, this is what I do. It works, but I don't think it is the "right" way. I put the iron on the back of the pot for a few seconds, then melt a good sized bead of solder on the back of the pot. The wire that is to go there is separately treated with solder, just enough to coat it and to run between the braids of the wire. Then I hold the wire against the solder bead and heat the two together until they fuse.
Remember two things: One, don't heat any sensitive component for too long (caps, pots). Otherwise, they'll fry. Two, make sure your soldered joints are shiny. If they are dull, that is a "cold joint" and must be redone.
Hope this helps. :icon_thumright: