The first thing I check on a cap is the underside of the brim, right where it meets the crown. If that seam is stiff and flat rather than curved, the cap sits like a lid instead of a cap, and no amount of adjusting the strap fixes that. A good brim has a slight natural curve already built in, so it sits low over the eyes without you having to bend it yourself for a week to get it to behave.
Sizing on caps is more forgiving than most hats because of the strap at the back, but there are still two ways to get it wrong. Too loose and the whole thing rocks on your head the second you look down to cross a road. Too tight and you get that pressure line across your forehead that shows up in every photo for the rest of the day. The snapback or velcro strap should sit flat against your head, not bunched up, and you want enough room at the crown that your hair isn't crushed flat the moment you take it off. If you have a lot of hair, go up a size or look for one with more adjustment range at the back, because the ones that only fit snug are miserable after an hour.
Where a cap stops being useful is anywhere you need it to look deliberate rather than practical. It's not doing much for you under bright office lighting or anywhere smart, and it won't save unwashed hair the way people hope, it just frames it differently. Cotton ones hold their shape for a season or two of regular wear and then start to soften at the brim, which some people like and some find scruffy. Thrown in a bag, the structured ones can end up with a crease across the brim that never fully drops out, so if you're carrying it rather than wearing it, look for one that's a bit more pliable to begin with. Washing is where most caps lose their shape for good, a hot wash will warp the brim and shrink the strap, so a cool hand wash or a careful machine cycle in a bag is worth the bother if you want it to last past one summer.
On colour, I've had the most use out of washed out neutrals, faded black, stone, a soft olive, because they don't show sun fade or sweat marks the way a crisp white or a bright colour does within a few wears. White looks brilliant for about three outings and then shows every mark at the sweatband. Darker, slightly worn in tones just age better and still look intentional months later.
Try it on and look down as if you're checking your phone, if the brim blocks your view completely, it's sitting too low and you'll be tilting your head back all day to see properly.