The warning first: the wrong fabric on a seam that sits in the wrong place will have you fishing it out in public within the hour, usually in a queue, usually when you're wearing something you can't easily adjust without looking deranged. Everyone who's dismissed thongs as a bad idea has usually just had the wrong one, in the wrong size, in lace that was never going to behave. Get the construction right and they solve a specific, recurring problem rather than being there to prove a point. No lines under anything fitted, no bunching, no fabric trying to escape round the sides of leggings. That's the whole job.
Think about what you're wearing over them before you think about the thong itself. Thick seams, ornate lace edges and anything with a visible bow or hardware will show through fine jersey, satin, or anything with a bit of cling, so save those for looser trousers or skirts where nobody's looking that closely. For dresses, leggings, fitted trousers or anything in a slippery fabric, you want a laser cut or bonded edge with no seam at all, and a front panel in a fabric that matches your skin tone rather than the bright white one that photographs as a bright white square. On colour, skin tone shades in your own undertone are the ones that disappear under everything, and a mid grey or soft nude does more work than black, which can show as a shadow under pale or light coloured clothing. Save the deep jewel tones and patterns for days when nothing's going over the top anyway. Fit matters more here than with almost anything else in a lingerie drawer, because the side straps need to sit flat against the hip bone rather than digging in, and the back strap width is personal, not a matter of toughness. If you're sizing by your knicker size normally, go down rather than up, since a thong that's loose at the hip will ride and twist, while one that's genuinely snug across the hip stays put all day. The rise matters too, a low rise under low waisted jeans, a higher one under anything that sits at the natural waist, and mixing those up is how you end up either showing a strap or feeling cut in half.
The one mistake worth avoiding entirely is buying a single size across every style and assuming it'll translate. A lace high leg and a cotton midi from the same size label can fit completely differently, and the only way to know is to actually try the specific cut you want before you buy five of them in one go.