The first thing I do with a chair cover is grab the fabric at the seam and pull, just a little, to see if it's got any give. A cover with zero stretch is going to fight you every single time you try to wrestle it onto a dining chair with arms, and you will know this fight intimately if you host more than four people a year. The good ones have a bit of spandex worked in so they snap back into shape instead of sitting there wrinkled like a bedsheet that lost an argument with the dryer.
Measuring is where most people get it wrong, me included, the first time I tried to cover six mismatched chairs I'd pulled from three different estate sales. You need the back height, the seat width at its widest point, and whether the chair has arms, because a cover sized for an armless chair will not stretch over an arm no matter how much you believe in it. Measure the tallest chair in the set if they're not identical, and expect a little extra fabric pooling at the base of the shorter ones rather than trying to find six separately sized covers and losing your mind over it.
Where covers fall short is on anything with a distinctive shape you actually like looking at. A carved wooden chair back, a nice curved spindle, anything with personality gets flattened into the same soft blob under a cover, so if the chair itself is the good part, cover it for one dinner and then take it right back off. They're also not much good in a sunny room you don't plan to launder often, because the fabric will fade unevenly in the patch that gets the afternoon light and you'll end up with one chair looking distinctly more tired than the rest of the set.
What they sit well with is an ordinary table that sees real use, weekday breakfasts, a toddler with a crayon, a dinner where someone inevitably knocks over the gravy. A plain cover in a color that's a shade lighter or darker than your walls reads as intentional rather than like you're hiding something, and it makes the room feel calmer in the low light of early evening, when mismatched chairs usually look their most chaotic. They're also the easiest fix I know for a thrifted dining set where every chair came from a different decade and none of them agree with each other.
The one mistake to avoid is buying before you've measured the arms. Guess on that and you'll spend an evening stretching fabric that was never going to reach.