The first thing I do with a zip hoodie is tug the zip itself, right to the top, and feel whether it catches or glides. That little pull is the whole story of the garment in miniature. A cheap zip snags on the chin fabric, sits slightly off centre once it's done up, and within a few washes starts gapping at the bottom no matter how still you stand. A good one closes in one smooth motion and sits flat against the body, and that single detail tells me more about the rest of the construction than anything printed on the label.
Past that zip, it's about what the fabric does when you're actually wearing it rather than holding it up under a shop light. A heavier loopback cotton has real weight and holds its shape through the day, it doesn't go thin and papery at the elbows after a winter of wear. Thinner fleece can feel soft in the hand but turns limp and see through once it's been washed a dozen times. The hood should sit with a bit of structure rather than collapsing flat the second you let go of it, and the ribbing at the cuffs and hem needs enough stretch to snap back, not stay baggy and stretched out by Christmas. Check the zip pull too, a solid metal one with a bit of heft lasts, a thin moulded plastic tab is usually the first thing to snap off, often right when you're trying to get out of it in a hurry.
On colour, the ones I keep reaching for are grey marl, navy, and a soft black that's been washed rather than starched stiff. They go under a coat, over a t-shirt, with jeans or leggings, and they never fight with anything else you've put on that day. Bright colours and bold prints look brilliant on the hanger and then sit in a drawer because they only work with about two outfits you own. Plain, slightly heathered shades earn more wear simply because they ask nothing of you.
If you're starting from nothing, go for a mid weight grey marl in a relaxed, not oversized, fit, something you can wear zipped right up on a cold school run or hanging open over a shirt without either version looking like you got dressed wrong. Everything else, the colour pops, the cropped ones, the statement zips, can come later once you know this is a shape that actually gets worn and not just bought. Does the zip glide first time, every time, or is it already catching before you've even paid for it?