Hi, Alex.

Better quality cables will not have a ground wire.

The cables from your turntable are carrying low level electrical signal determined by the output voltage of your cartridge.

Low level signals are typically more susceptible to interference generated from adjacent electronic equipment & cables.

Look for cables that have good shielding characteristics.

I recommend you get a set of good quality shielded RCA cables from someplace like Blue Jeans Cable

You don't need to spend ridiculous amounts of money to get decent cables.

As for the ground wire, any small gauge wire from your local hardware will work fine, or just peel off the ground wire from the bundle you already have.

Bill

Edit: Here is an upgrade you may be interested in:  LINK

I suggest the Audioquest Evergreen cables.

It is best to keep the cables from the turntable to phono preamp under 3 feet if possible. Longer cables have too much capacitance and can affect the sound of the cartridge.

Just use a piece of ordinary 16 or 18 gauge stranded wire for the ground wire.

It is usually helpful to crimp or solder a spade lug on each end, which can be screwed down readily.