In volleyball, you need shoes with a lot of traction. There are some regular shoes out there with traction, but you would probably be better off with actually volleyball shoes. However, if you're just starting out or on a recreation team, you don't really need volleyball shoes, I would wait until middle school before buying them to make sure they like the sport before spending a lot of money. But if you feel more comfortable if your child has volleyball shoes or they would want them, I would recommend just getting discount volleyball shoes. Discount volleyball shoes don't have defects or anything, it is usually last year's style and they're coming out with a new one.
Also, if you're child or you don't feel comfortable with last year's style and buying discount volleyball shoes, you can always find cheap namebrand volleyball shoes if you look hard enough. These may take longer to find, but you will find some eventually. However, if you want to spoil your child or feel they need the best, you can buy them women's adidas volleyball shoes or any other namebrand you feel up to buying. Whatever type of shoes you buy, good luck out on the courts!