Different qualities aren't limited only to wild pets—many rare World drops and special non-wild companions have had their stats boosted. For example, the world-drop dragon whelps (Azure Whelpling, Crimson Whelpling, Dark Whelpling, and Emerald Whelpling) are of [rare] quality. Check your Pet Journal to see the color-coded rarity of your non-wild pets.
The vanilla WoW Horde leveling guide you see on this site was originally made back in 2006 by Joana (AKA Mancow, or FuriousPaul). The guides have been tweaked many times over the years to make things "faster". The leveling guides were made because of all the messages I got from people asking me how I was able to level up so quickly on new realms. I was first to level 60 on 7 different realms (3 with Mancow and 4 with Joana), even winning Blizzard's "First to Level 50" contest they held back in 2006.
2. Achieving. There are many pet battling achievements in game, and following the natural trail through the Taming [Continent] achievements up to Pandaria, and then on to the Spirit Tamers, Beasts of Fable and the Celestial Tournament was an epic journey for me and for many others. It's well worth doing. The Celestial Tournament is still, IMO, the pinnacle of PvE pet battling. However, WoD and Legion and BfA have added more battling achievements.