While you have the option of buying different furniture to mix and match, there's a bigger advantage if you buy a 3 piece living room set. This idea might be surprising, but it's true. For example, it's a lot more convenient to shop for a 3 piece living room set than buying separate pieces. You'll likely have to deal with one vendor, and you can save on shipping charges.
Another advantage is that you get consistent craftsmanship on the different furniture in the set. Keep in mind craftsmanship can vary a wide lot. And, it would be silly to see your table come with high craftsmanship while the chairs come with a poor one. If you buy a 3-piece set, then its made from one manufacturer and you don't have to worry about the variance in the craftsmanship. Another advantage of buying a set is that you may get a better deal. Think of it as similar to a wholesale discount. Since you are buying in more volume, you'll often save money compared to buying piece by piece when all things are equal.
While a 3 piece living room set may have plenty of advantages, you still have to consider a few factors. For example, it's extremely important that you get the size right, and that means doing some measurements. You also need to know the kind of configuration you need for a 3 piece living room set.
Do you need a table or an ottoman? Do you need same-sized couches? It's best that you figure these factors out before you go shopping if you want to save time and money.