The thread count on the package is almost never the number that matters, and that trips up more people than it should. A 600 thread count sheet made with cheap short staple cotton will pill and go thin faster than a well made 300 thread count one, so you end up paying for a number instead of a feel. It still matters more than almost anything else in the bedroom, because you touch it for eight hours a night and you notice a bad sheet a lot faster than you notice a bad side table.
A full matching set makes the most sense in a bedroom that is otherwise fairly plain, where the bed is the main event and you want it to look finished without hanging art or picking a wall color. In a small room, go lighter rather than heavier, a dark heavy duvet set can make a cramped space feel like it is closing in, while a lighter sheet and a simple cover leaves the room feeling like there is still air in it. Summer wants something that breathes, cotton percale or linen, winter wants weight and warmth, flannel or a thicker weave, and if you are starting from nothing I would buy two sheet sets in a plain color before I bought one patterned bedding set, because plain sheets work under anything you add later and a patterned set locks you into one look until it wears out. Pillowcases are the cheapest way to change the feel of a room between seasons, so buy a few extra pairs before you spend on anything else.
Where this goes wrong is when people buy the matching bedroom set thinking it will solve the whole room, curtains and all, and end up with everything from the same three colors looking flat and a little like a hotel that is trying too hard. It is also the wrong place to go cheap if you have allergies or run hot at night, a scratchy low grade sheet will have you kicking it off by two in the morning no matter how nice the pattern looked online, and a fitted sheet that is the wrong depth for your mattress will be fighting its way off the corner by week two. If you have a thick mattress topper, check the pocket depth before you buy, that one detail has ruined more otherwise good sheet sets than anything else.
This is the easiest upgrade in any house, rented or owned, old mattress or new, and it suits a home where the bedroom is meant to feel calm rather than decorated.