Standard weight sets are often used for small weight lifting setups in homes, usually consisting of just a bench and one of these weight sets. Additional standard weight plates can easily be added later and are available from this site and many other places.
These weight sets are the most economical barbell sets you can get. The recommended weight limit on the bars is usually around 200 lbs, so if you're lifting more than that you should think about getting an olympic weight set instead.
Even people who have olympic weights sometimes get standard dumbbell handles and weights, because the shorter standard dumbbell handles are more maneuverable than olympic dumbbell handles. Particularly people often find that olympic dumbbell handles hit each other too easily on the top of the rep of a bench press or military press, so the standard handles allow a freer range of motion.
Standard weights also have a low starting weight, making them a decent choice for youths and women where start-up costs are the biggest factor and long-term commitment hasn't been decided upon.