Shorts are the one summer buy people get wrong every single year, because they panic about their legs instead of thinking about the fabric and the cut. Sort those two things first and the rest looks after itself.
Stick to colours that don't ask questions: navy, washed denim, a soft khaki, black if you want something that pairs with everything you already own and makes no decisions for you in the morning. White is lovely for about three wears before it needs a wash it may not survive, so I'd leave that one until you've got the rest sorted. If you're starting from nothing, go for a pair in a cotton or denim blend with a bit of give in the waistband, a length that sits somewhere around mid thigh rather than committing hard to short or long, because that's the one that goes under a loose shirt to the shops and under a linen top to something slightly nicer without you owning two pairs. In the shop, forget how they look standing still and sit down in them, that's where you find out if the waistband digs or the inseam rides. Check the pockets actually open rather than being sewn shut for shape, check what happens when you bend over, because a lot of tailored pairs look sharp on the hanger and show everything the second you pick something up off the floor. Linen ones need checking for lining, since some are see through enough to need a slip underneath, which nobody tells you until you're stood under a shop light wondering why the assistant's gone quiet. Jersey shorts are brilliant for travel and lounging but check the hem doesn't curl after one wash, that's the tell for cheap jersey. These earn their keep from late spring through to the end of summer, good for a garden, a barbecue, travelling, a hot commute, anything where trousers would be a mistake and a dress feels like too much effort. Tailored pairs can do a smart lunch or an office with air conditioning that's clearly been set by someone who's never worn tights. Denim ones are for every single day you can get away with it, which in a good summer is most of them.
Tomorrow morning I'd put a pair of khaki cotton shorts on with a plain white t shirt, trainers, and a denim shirt left open in case the weather hasn't made its mind up, which round here it rarely has.