Sports bras have a reputation for being either so flimsy they do nothing or so tight they leave you looking like you've been vacuum packed. I have worn both kinds, often in the same week, and I think the good ones are a bit undersold by how boring they look folded on a shelf.
For most of the year a medium support one covers almost everything you need, walking, weights, a gentle jog that's really more of a fast walk when you remember your knees. Winter is when you notice the fabric more, because you're layering a t-shirt or a zip top over it and it needs to sit flat without a seam printing through, and summer is when you notice the straps, because they're the only thing anyone sees once the top comes off at the end of a run. If you've got none at all and you're starting from scratch, go for the medium support option in a size that feels snug when you put it on rather than one you're hoping will loosen up, because they don't loosen up, they just go. A high support one is worth having for anything that involves actual bouncing, but you don't need to start there, it's the second bra you buy, not the first.
In an ordinary wardrobe it does more jobs than the label suggests. It goes under a loose t-shirt for the school run or the supermarket, it goes under a vest top for the gym without needing anything else, and a plain one in black or grey works under a thin white tee when you want the shape without a normal bra's straps showing. What it doesn't get on with is anything with a low back or an open side, because the wide band that makes it supportive is exactly the bit that shows, and there's no outfit where a thick grey strap peeking out the back of a nice top looks deliberate. It also doesn't suit being worn under really fitted knitwear if it's got any padding or moulded cups, because you'll get two distinct circles instead of a smooth line, and that's a look nobody's going for outside of a gym.
Start with grey or a mid tone rather than black. It shows less under pale tops, hides sweat marks better than you'd expect, and it doesn't fade into that slightly green tinge black ones get after enough washes on a hot cycle.