An oversized shirt is the thing you put on when you want to look like you've made an effort without actually making one. It works over trousers, over leggings, belted as a dress, or thrown on top of whatever you wore to bed. The job is simple: structure without a fitted shoulder, and room to move without looking like you've borrowed someone's.
The difference between a good one and a dreadful one shows up fast if you know where to feel for it. Cheap cotton goes thin and see through within a few washes, so hold it up to the light in the shop, properly, not a polite glance. The collar should have some body to it, not flop the moment you touch it, and the buttonholes should be neat rather than frayed at the edges, because that's usually the first thing to go. Check the side seams too. A proper oversized shirt is cut generously on purpose, with the extra fabric falling from the shoulder in a deliberate way, which is different from a shirt that's simply too big because someone got the pattern wrong. Feel the weight of it in your hand. If it feels like nothing, it'll probably wear like nothing within a year, however nice it looks on the rail.
If you're starting with none, go for white or a pale blue before anything patterned or coloured. It's the version that does the most jobs with the least thought, tucked loosely into jeans for one day, worn open over a vest the next, and it photographs well under nothing more complicated than daylight through a window, which matters more than it should. Once you've got that one bedded in, a stripe or a soft check is the sensible second buy, because it still behaves the same way but gives you something to talk about.
It sits happily over narrow trousers, cycling shorts, a plain skirt, or jeans with the cuffs rolled, and it's one of the few shirts that genuinely improves with a belt, since the shape it creates at the waist is most of the point of wearing it oversized in the first place. Before you buy, check the shoulder seam sits where you want the drop to actually drop, not three inches further down than looks deliberate, and check the fabric doesn't go sheer when stretched across the back, which is a cheap trick some of them try to get away with. Reach for it on the mornings when you haven't decided what the day is yet, and need one thing that will decide it for you.