A black top is the thing you reach for when you can't decide what else to wear, or when you've decided something else and it's gone wrong, or when you just need one piece that doesn't ask any questions of the rest of the outfit. It sits under jackets, over vest tops, under dungarees, and it's supposed to disappear into whatever job you're asking it to do. That's the whole point of it.
The difference between a good one and a bad one shows up fast, usually the first time you move your arms. A decent fabric has a bit of weight to it, enough that it skims rather than clings, and it holds its shape wash after wash instead of going see through and baggy at the same time, which somehow does happen. Check the seams at the shoulder and underarm, they should lie flat, not pucker. Cheap black fades to a flat grey after a few washes because the dye hasn't gone deep enough, so run your hand over it in the shop, if it feels thin and slightly plasticky under the lights, it'll look worse under daylight at home.
Before you buy, check the neckline sits where you want it when you lift your arms, not just when you're standing still in front of a mirror doing nothing. Check the hem, some black tops are cut long for layering and some are cropped enough to show a strip of midriff you weren't expecting. Hold it up to a window if you can, cheaper jersey is often more sheer than the label lets on, and nobody wants to find that out at a bus stop.
It's the wrong choice when you need texture or personality doing the talking, a plain black top under a plain black blazer can read as trying very hard to look like you haven't tried. It's also not the one for anything that needs structure, a soft jersey top won't hold a shape the way a shirt does, so if you need sharp, look elsewhere.
On shades, true black is the easiest to match with other black, obviously, but a lot of "black" tops are actually a warm charcoal or a faded black, which looks odd next to proper black trousers. A slightly softer, almost washed black is kinder in daylight and doesn't show lint and dust the way a deep black does, worth knowing if you're wearing it with a coat that moults.
Wash it inside out, on a cool cycle, and keep it away from anything shedding white fluff in the same load.