I just had to "upgrade" the power cable on my Garrard 301. The 57-year old 18 gauge power cord separated where the molded on power plug was attached and it stopped working.
I replaced the power cord with about 2 feet of 18 gauge stranded quality lamp cord with a molded on plug. It's black rather than the original brown, and the insulation is thicker and more flexible. Looks a lot better, and guess what, the soundstage has widened, the PRAT qualities of the 301 are amplified, and the bass has improved.
And if you believe that, I have some Elite Fairy Fur power cables to sell for $250 per foot, with Hospital grade plugs on them. (Note! No fairies are harmed in the production of Elite Fairy Fur Power Cables. They get monthly haircuts, which they enjoy, because they are fashionable elite fairies. The fur is woven by means of a magical process called Rapunzel Braiding, which literally sucks the electricity through the cables. You do have to turn the volume up a little to cover the refined slurping sound the cable makes sucking the electrons)
I spent nothing on my cord, because the cord that I used was a spare end that I had lying around. I got a nice looking installation at no cost, and, I got reliable power to the turntable, which certainly beat the old connection, which didn't work at all. I can't afford to buy the Fairy Fur Cables. Don't make enough money selling them. That's why they are $250 per foot.
I don't think I need anything more than 18 for my inferior record player. It doesn't seem to be starving for current. And, as others have said, the 20-amp circuit that I run my stereo off uses 12 gauge Romex in the walls. The short cable that hooks the turntable to the wall does not have that much of an effect.
But anyway, that said, get some decent 18 gauge, or if you want way overkill, 16 gauge wire, and hook it up carefully to a decent wall plug. That should get the job done.
And good luck from the old purveyor of fairy fur,