Do linen shorts crease the second you sit down? Yes, a bit, and that is the whole point. The crease is what tells you it is actually linen and not a polyester blend pretending, and once you stop fighting it, these become one of the easiest things you own in warm weather.
I reach for mine from late spring right through to the end of a hot September, for anything that doesn't need ironing out properly, which is most of life. A weekend lunch outside, a long walk somewhere with no shade, sitting on a train with the sun coming through the window for two hours. They are no good for anything formal, the linen is too relaxed for that and will always look a little slept in, but that softness is exactly why they work for the in between days when jeans feel wrong and a dress feels like too much effort. On colour, I have learned to avoid anything too pale after one memorable afternoon in cream ones that showed every blade of grass and a bit of ketchup before lunch was even finished. Stone, olive, a faded navy, a soft rust, these hide the real life a pair of shorts goes through and still look deliberate rather than tired by August. White looks lovely on a hanger and on nobody's actual Tuesday. For pairing, I live in mine with a simple vest and flat sandals for daytime, then swap the vest for a linen shirt worn open over a plain top if the evening turns slightly cooler, which it always does. They also sit well under a longer linen or cotton shirt left unbuttoned, so you get the look of trousers with the comfort of something that has no waistband drama in it at all.
The thing that actually sold me on good ones is how they hold up, not how they look fresh out of a bag. Cheap linen shorts go thin at the inner thigh within a season and the hem starts to fray in a way that looks accidental rather than nice. A better weight of linen softens instead of wearing through, comes out of a machine wash a bit creased but structurally the same pair of shorts, and packs down small enough for a weekend bag without sulking about it. Mine have been balled up in the bottom of a bag more times than I'd like to admit and they have never once looked as bad as I expected when I shook them out.
Check the weight of the fabric first, between your fingers rather than on the label, since too light means see through in sunlight and too heavy means they never really soften.