You can spot a good asymmetric dress from the other side of a room because the hem does something interesting without you noticing how. One shoulder bare, the other covered, a diagonal that cuts across the body and skims rather than clings. The poor version just looks like a regular dress that someone forgot to finish, an uneven hem that reads as a mistake rather than a design, and a shoulder strap that slides down every twenty minutes and makes you look like you're fighting your own outfit all evening.
If you're starting from nothing, go for one with an asymmetric neckline rather than an asymmetric hem, because it's easier to wear with normal shoes and normal tights and doesn't need you to think about leg positioning every time you sit down. A single bare shoulder in a mid weight jersey is the most forgiving shape going, it moves with you rather than needing you to hold still, and it works under a coat in a way a dramatic cut out hem never will. For colour, go plain and solid before you go anywhere near a print, because the asymmetry is already doing the interesting bit and a busy pattern fighting with an uneven hemline just looks confused. Deep green, black, a rich berry, any of those photograph well and don't show much against a dark pub carpet or a slightly dodgy wedding marquee floor. Pale colours show every mark and make the asymmetric cut look lopsided rather than deliberate, which is the opposite of what you want.
Jersey and matte crepe age the best of any fabric I've tried in this shape, they don't crease in a bag the way satin does and they don't pill under the arm where a bag strap sits all day. Wash it inside out on a cool cycle and skip the tumble dryer, because heat is what kills the stretch that holds an off shoulder neckline in place, and once that goes the whole dress sags rather than sits. A dress that's lasted me two summers of actual wear still holds its shape because the fabric has a bit of weight to it rather than feeling like a bin bag.
The real difference between a brilliant one and a disappointing one is in the hem and the seams, not the fabric alone. A proper one has a weighted or bound hem so the diagonal edge doesn't curl or fray after a few washes, and the shoulder seam is reinforced rather than just overlocked, because that's the point that takes all the strain when you reach for a drink or shrug off a cardigan. Cheap zips split exactly where the asymmetric seam meets the side, so check that bit before anything else.