There is not really any best order, as you already know The Lion King is the first film in franchise and The Lion King II: Simba's Pride is the sequel, so that's the order which matters. The Lion King 1½ take place before, during and after The Lion King, so you should watch it after The Lion King but not necessarily before or after The Lion King II.
According to the Lion King Fan Wiki, The Outsiders were an offshoot of Simba's pride, who decided to remain loyal to Scar after his death. We are suppose to assume that they were there during the course of the first film and that not all of the lionesses supported Simba after all.
Outsiders (also known as Outlanders) are an offshoot of Simba's pride.