Answer by taking a quote from the following article:

Oscar Gutierrez (born December 11, 1974), better known by his ring name Rey Mysterio Jr. or simply Rey Mysterio (Spanish for "King Mystery"), is an American professional wrestler who is currently wrestling on the independent circuit. Mysterio is best known for his appearances with Extreme Championship Wrestling, World Championship Wrestling and WWE between 1995 and 2015, becoming a three-time world champion in the latter. Widely regarded as the greatest cruiserweight wrestler of all time,, Mysterio is known for his high-flying Lucha libre wrestling style, which is credited with having helped kick-start the emergence of cruiserweight wrestling in the United States in the mid-1990s. Championships held by Mysterio over the course of his career include WWE's World Heavyweight Championship, the WWE Championship, WCW/WWE Cruiserweight Championship, WCW World Tag Team Championship, WCW Cruiserweight Tag Team Championship, WWC World Junior Heavyweight Championship, WWE Tag Team Championship, and WWE Intercontinental Championship.

Mysterio made his World Championship Wrestling (WCW) debut on June 16, 1996, at The Great American Bash, challenging Dean Malenko for the WCW Cruiserweight Championship, which Malenko retained by winning. In July at Bash at the Beach, he defeated longtime rival Psicosis in a number one contender's match to earn another opportunity at the Cruiserweight title. The next night, on the July 8 episode of WCW Monday Nitro, he defeated Malenko to win his first Cruiserweight Championship. He reigned as champion for three months, which included title defenses against the likes of Ultimate Dragon, Malenko, and Super Calo before he lost the title to Malenko at Halloween Havoc. Following his Cruiserweight Championship reign, Mysterio challenged Ultimate Dragon for the J-Crown Championship, but was unsuccessful in his title match at World War 3 in November.  In early 1997, he feuded with Prince Iaukea over the WCW World Television Championship. Mysterio was defeated in his title match against Iaukea at SuperBrawl VII after Lord Steven Regal attacked him. Mysterio also lost a championship rematch at Uncensored in March. Mysterio soon began a feud with the New World Order (nWo), which culminated when he lost a Mexican Death match to nWo member Konnan at Road Wild in August. Mysterio then became involved in a feud with his real-life friend and Cruiserweight Champion Eddie Guerrero. He defeated Guerrero in a Title vs. Mask match at Halloween Havoc to win the Cruiserweight Championship for the second time. On the November 10, 1997, episode of Nitro, he lost the title back to Guerrero. They had a rematch at World War 3, which Mysterio also lost.  On the January 15, 1998, episode of WCW Thunder, Mysterio defeated Juventud to win his third Cruiserweight Championship, but lost it nine days later to Chris Jericho at Souled Out. After the match, Jericho continued the beating by using a toolbox he found at ringside. This storyline was used to cover Mysterio's need for a knee operation that kept him out of the ring for six months. He made his return at Bash at the Beach, where he defeated Jericho for his fourth Cruiserweight championship. The next night, however, the result was overturned and the belt returned to Jericho due to Dean Malenko interfering. Later that year, Eddie Guerrero formed a Mexican stable known as the Latino World Order (LWO) (a spin off of New World Order) that included nearly every luchador in the promotion. Mysterio continually refused to join and feuded with Guerrero and the LWO members, including winning a match against longtime rival and LWO member Psicosis in a match at Road Wild. He was finally forced to join the group after losing a match to Eddie Guerrero. Mysterio's on-and-off tag team partner Billy Kidman joined him during the feud with LWO, wrestling against the LWO despite Mysterio being a part of the group. His alliance with Kidman was formed after Mysterio helped Kidman defeat Juventud for the Cruiserweight Championship at World War 3. Mysterio went up against Kidman for the title at Starrcade but was unsuccessful winning back the title in a triangle match that also involved Juventud. Kidman once again defeated Mysterio for the title at Souled Out in a fatal four-way match that also included Psicosis and Juventud.

Did he start his career in the Cruiserweight division?
debut on June 16, 1996, at The Great American Bash, challenging Dean Malenko for the WCW Cruiserweight Championship,