BasicDataSource is, as the javadoc says, a one-stop shopping for basic needs. It has all the necessary. It creates internally a PoolableDataSource and an ObjectPool.
PoolingDataSource implements the DataSource interface using a provided ObjectPool. PoolingDatasource take cares of whatever has to do with connections (casting, checking validity, setting properties, etc) and ObjectPool take cares of holding and counting this whatever-type-it-is object.
So I should use BasicDataSource. If you need something special maybe can use PoolingDatasource with another implementation of ObjectPool. But I think it would be a rare case.