3/4 drums are usually for children up to 7 years old, due to the smaller size kit, making the playing more comfortable for them. When children reach 8 years old and an average height, they can move up to a full-size drum kit, which is great due to the longevity of the kit as adults can play it too meaning you won't need to repurchase for a while!
The two most popular drum kits are called 'rock' and 'fusion'. A rock kit usually has a 22" bass drum 12", 13" and 16" toms and a 14" snare on a normal 5 piece kit and is designed for the rock drummer. A fusion kit usually has a 20" bass drum 10", 12" and 14" Toms and a 14" snare on a normal 5 piece kit and designed for the jazz-funk drummer.