Hi Oli, presume you are doing a Strat?

First and foremost is to make sure all pots have ground wires soldered to each other, like in a daisy chain. To rely on just the copper tape may not work very well.

Shielded wire? I have used mostly vintage push back cloth wire and never bothered with the braided shielded wire as most of my builds have have required quite short lengths of wires, except for the just finished ES1 where some lengths were between 20cm & 30cm with no earth buzzing issues. In fact no copper tape was used anywhere at all on that build.

Some folks reckon braided stuff is better where there is a long run up to a 3 way switch as in LP's and that may be true. I just prefer to run a separate hot, separate ground and not too keen on inner & outer core stuff as invariably the outer screen stuff is the weakest point and can let you down.