A 15 pound baby should wear a size 1 diaper although some 15 year old babies may need to wear a size 2 diaper depending on the diaper.
Some diaper brands run larger than others.
The most sold diaper size is a size 4 diaper which is what most kids wear until they are potty trained.
Rarely does a kid need a size 5 or size 6 diaper unless they are larger than average or they don't potty train soon enough.
Size 4 diapers can fit most average sized toddlers and kids up to 3 years old.
After 3 years old the child may need a size 5 or size 6 diaper.
After 4 years old a child may need a size 6 diaper or size 7 diaper.
If you have limited space, the bulk of your diaper collection should be for sizes 1 and 2.
These diapers generally fit babies up to 18 pounds, depending on the brand.
If you have the storage you should also get Size 3, as well, which should take you through your baby's first birthday.
Some diaper brands run larger than other diaper brands so while a baby or toddler may fit in one diaper brand in a size 6 they may not be able to fit in the same size 6 diaper in another brand.
Pampers baby dry and Luvs as well as Gentle Steps diapers tend to run larger than other diapers such as Parents choice diapers.
Even Rascal and Friends diapers run larger and size 6 Rascal and Friends diapers could fit kids up to 3 or even 6 to 7 years old.