Pink has a reputation for being a bit much, a bit sweet, a colour you wear once in your twenties and then quietly retire. I think that's unfair on the skirt itself. Worn right, a pink skirt is no fussier than a navy one, it just photographs louder, which isn't the same thing as being harder to wear.
If you've never owned one, start with something in a solid, mid weight fabric rather than anything floaty or sheer, a straight or A line shape in a dusty or blush shade rather than anything bright. That version goes with the grey, white and denim you already own, and it won't feel like a costume the first time you wear it. Save the bold fuchsia or coral for later, once you know how much pink you actually want in your life.
On shade, the easiest colours to live with sit somewhere between dusty rose and a pale, slightly muted blush, the kind that could almost pass as neutral in low light. Anything with grey or brown mixed into the pink wears better across more seasons and more skin tones than a pure, sweet shade, which can tip into looking like fancy dress under certain lighting. Bright pink is lovely but it wants confidence and a plain top, it isn't a colour that quietly blends in, and you should only buy it if you're happy to be looked at.
The difference between a good one and a disappointing one is mostly in the fabric and the finish. A cheap pink skirt often uses a thin, slightly shiny synthetic that creases the moment you sit down and shows every seam from the inside. A better one has some weight to it, a proper lining if it's at all sheer, and a waistband that sits flat rather than rolling. Check the stitching at the zip and hem before you buy, pull gently at the seams, and have a look at the lining fabric if there is one, since that's usually where the corners get cut.
In the shop, hold the skirt up to a window if you can, pink shows every flaw in bad light that it hides under shop spotlights. Check how it falls when you walk, not just when you stand still, and feel the fabric between your fingers for any papery thinness. Pink works through spring and summer without much effort, and struggles a little in deep winter unless the fabric has real substance, so think about what you'll actually be wearing it with before the clocks go back.
Wash pale pink separately for the first few cycles, just in case the dye hasn't quite settled.