Socks used to be the thing you bought in a multipack and never thought about again, but the better ranges now actually fit the shoe you're wearing them with, which sounds obvious and somehow took the high street decades to work out. On the whole, that's an improvement, though it does mean the bad ones stand out more than they used to.
If you're starting from nothing, go for a plain cotton ankle sock in a rib knit, the kind that sits just above the shoe line without disappearing into it. That's the length that works with trainers, flat boots and loafers, which covers most of what anyone actually wears on a normal day, and it's the easiest one to build out from once you know what you like. Black and a mid grey are the shades that cause no trouble at all, they go under boots with jeans, under trainers with a dress, and they don't show through thin trousers the way white and pale colours sometimes do. White is worth having too, but only for trainers, because anywhere else it reads as sportswear whether you meant it to or not. Before you buy, check where the heel is shaped, a lot of cheaper socks have a straight tube foot with no heel pocket, and that's what causes the bunching and the sliding, not the size of your foot. Check the top band as well, pull it gently, if it springs back sharply it'll dig in by midafternoon, if it barely moves at all it'll be round your ankle by lunchtime.
The difference between a sock that lasts and one that's thin and shapeless after a few washes mostly comes down to the cotton content and how much stretch fibre is mixed in. A high cotton percentage with a small amount of elastane holds its shape wash after wash, where a cheaper cotton blend goes baggy at the ankle and never quite recovers. Look at the toe seam too, a flat seam lies invisible under the toes, a bulky one you'll feel inside a shoe within the hour, especially in anything fitted like a trainer or a ballet flat. Knee highs are worth the same scrutiny at the top, the band needs to be firm enough to stay up under a skirt without leaving a mark you're still looking at in the evening.
Start with a plain mid grey, it goes with more than black does and shows far less wear.