The fresher the better. Eggs in supermarkets don't even have half the flavor of fresh eggs. Try to make some time and head to the nearest farmer's market and treat yourself to some farm fresh eggs. They may be pricier but you get every cent back in flavor and a golden orange yolk.
Egg Salad Cooking Tip
With eggs, cooking at a low temperature is almost always preferred. It allows the eggs to keep better texture. Also if you ever mix your uncooked and hard boiled eggs, do not fret. A trick to distinguish the two is a spin on the counter top. Hard boiled eggs will spin with ease while uncooked eggs won't get any momentum.