If you're holding a sleeveless top in the changing room, the first thing I'd ask is how it sits across the chest when your arm is raised above your head. Reach up like you're getting something off a high shelf. If the armhole gapes open and you can see straight down to your bra, that's not a fault you'll fix later, that's just the top, and you'll be tugging at it all day every day you wear it.
While you're in there, check the armhole binding doesn't dig in when you bring your arms forward, the kind of movement you do a hundred times a day without noticing, reaching for a bag strap or a cupboard door. Press the fabric against your chest too, held up to the light if you can, because a lot of sleeveless tops are thinner than their long sleeved cousins and you want to know now whether you're going to need a vest under it before you've worn it out once and found out the hard way. As for what it clashes with, a structured blazer with a high armhole can fight the line of the top underneath and make the whole shoulder area look bulky rather than neat, and a bra with wide straps that won't tuck under a slim strap is going to show no matter how carefully you angle yourself in a mirror. Skip anything with a fussy neckline of its own if the top already has a strong one, you end up with two competing shapes instead of one that works.
Where it falls down honestly is in cold weather, obviously, but also in anything that needs sustained arm movement without a layer, carrying shopping any distance, cycling, a day that swings between an overheated train and a freezing platform. It's not a travel top either, nothing to roll into a bag and shake out looking fine, sleeveless pieces tend to crease right across the chest and sit oddly until they've had a proper hang. And if you're self conscious about your upper arms on a particular day, this is not the top that's going to talk you round, no shaping or print does that job, you either feel alright in it or you reach for something with a sleeve instead.
Worn well, though, a decent one holds its shape for a long while. Cotton blends soften and get comfier with washing, viscose ones can go a bit limp around the neckline after a year of wear and start pulling slightly at the shoulder seams, which is worth knowing before you buy five in different colours. Wash on a cool cycle, dry flat rather than on a hanger if the fabric has any weight to it, because a wet sleeveless top on a hanger stretches at the shoulders in a way you only notice once it's too late. It will never be the thing that keeps you warm, and it was never meant to be.