No thicker than 12 though, 14 is fine it will generally be faster possibly better resolution. You would be surprised that a "relatively" thin gauge would be better compared to all those fire hoses that are being pushed. If you look at the leads after cutting away the Insulating fillers and rfi rmi rejection layers that the wires are the same 14G size mutifilaments you take off the lamp wire spindle.
However if you want something really different and can percieve 1 part in a million impurity get the 8 "nines" wires. I can't hear it, but different coppers do seem to have an impact e.g. single crystal (OHNO) cast copper.
It is difficult to dissect the changesimposed by the hoses from the metals. I do think that silver is really quite different sounding than copper. People wiser than I say the usual cliches are bull. I can't understand why silver wires do have a sonic character in virtually every instance that I employ them that is reproducible in my mind all Physics aside. Except for the very least expensive ICs silver is not a budget friendly choice, nor is any patented alloy using Silver, Irridium , Palladium, Platinum, Tantulum, tempertamperum, Gold, Molybdenem......even aluminum is going to multiply the cost to high to stratospheric levels.
BTW avoid the heavy metals the radiation (gamma) makes me nauseas.
That said Wire does make your system sound different. I didn't believe it so me and my equally skeptical buddy tried out a good selection of speaker cables and the differences weren't subtle. The good part was -for that system,- on that day we agreed completely on the winner. It was of course the least expensive cable in the pile. (No Lamp Cord was tried as I recall sorry)