Wally's first Pokemon was a Ralts that Ruby loaned him, and a Kecleon he caught himself. His "starter" Pokemon was a Treecko which he rescued after Professor Birch lost it in a flood.
Wally asked Norman to teach him about Pokemon and help him catch one, but Norman refused after seeing how sickly Wally was.
Ruby seemed to take quickly to Wally, possibly because Norman didn't like Wally, and decided to help the other boy. Ruby loaned Wally his Ralts, nicknamed "Ruru", and Wally was able to capture a Kecleon.
Unfortunately, before Ruru could be returned to her rightful owner, an earthquake caused Ruby to fall into the sea.
The next time Wally is seen, he is rescuing the old man who looks for Mirage Island in Pacifidlog Town, from Kyogre's flood. It would seem that Wally had managed to recover much from his illness by then, and had been traveling around Hoenn for quite some time.
Norman, who had just been passing by, finally agreed to take Wally on as a student, and told him to come to the Sky Pillar.
There, Norman revealed that what he had been training Ruby for since he was very young was to help Norman awaken Rayquaza. Norman could only accomplish this with someone the size of a 10-year old boy.
Even though he's healthier, Wally wears a suit with a respirator built into it, showing that his sickness could be some form of asthma.
Wally acquired his Cacnea while traveling through the desert, his Roselia on Route 117, and Norman gave him his Flygon. Most of this occurred off-panel.
Wally was once believed to be a representation of Emerald because of his all-green team and mainly green wardrobe. However, he's not a Pokedex Holder and he debuted long before any announcements of Pokemon Emerald appeared, which means he was never intended to be Emerald representation. Due to that, a new character was created for that role.