If I may, let me add one exception to that.jal_ut wrote:...
"Should I cover the plant entirely?"
I never cover the plant. I add 2 or 3 inches of soil mounded up around the plant. I only do this one time. .
If you have potato plants coming up in the Spring, and a "late frost" threatens ... you can cover the entire (small) plant with soil. That protects the plant from the frost, and it will grow right back through the soil within a day or two.