Best wire strippers is a Bic lighter. Seriously, you cut zero wires that way. Can't believe how many years I fought stripping wires till son started playing guitar, I started going to guitar forums...
I like a solder gun. It heats up instantly, cools down quick. If you get an iron, get a soldering station. Has the springy thing to set your iron in and, a sponge. The stuff inside the solder builds up on your iron, becomes an insulator if you don't keep cleaning it. One more reason I like the gun.
Your biggest challenge will be getting the grounds soldered to the back of the pot. If you are not changing the pots, you can leave a little wire on them and, solder to that.
Don't have a clue what kind of solder, whatever RadioShack has.