There are some wires that are superior, but its mostly for durability and life, not sound. Oxygen free wires wont sound better (at first) but sure as hell, the normal copper wires will corrode and degrade over time. Shielding can have an effect on some things as well.
That said, I only use oxygen free expensive cables for musical instruments. For at home use, lowes sells "off cuts" for literally pennies a foot. I use 12 gauge for most of my things simply because I bought 100 feet of all copper wire for 7$.
Lamp wire doesnt work "about as well". Its literally the same damn thing. Theres absolutely nothing in that wire thats not in a lamp wire. Copper core, wrapped in epoxy/plastic/vinyl/whatever. Same thing 100% (minus the shielded and oxygen free wires which arent even being discussed).
edit: copper is copper mate. If your "home depot wire" was "going green" after a short time, any copper core speaker cable will follow suit... the ONLY way is to either tin (Which I personally dislike) or get some adapters for the ends.