Born in Yecla, Region of Murcia, Puche began his senior career with Elche CF, being almost exclusively associated with the reserves during his spell. He made his first-team debut at only 16, playing eight minutes in a 1–1 La Liga away draw against CA Osasuna; legendary László Kubala handed him his first opportunity with the professionals.
In the 1993 summer, after a spell with Valencia CF's B-team, Puche joined Palamós CF in Segunda División. He had a breakthrough year in his second season, scoring 21 goals to lead all players but being relegated due to the Catalan club's financial problems; on 9 April 1995 he netted six past CD Leganés – also eventually relegated – in a 7–1 home routing.
Puche continued competing in the second level in the following campaigns, with Villarreal CF, CD Toledo and Real Jaén. He retired in June 2004 at nearly 32 years of age, after several years in the lower leagues.
From 2005 to 2007, Puche worked as director of football at Cádiz CF. The following year he had his first senior experience in head coaching, with Tercera División's Xerez CD B, as well as also sharing directorial duties in the first team with former club player Antonio Poyatos.
In 2008–09, Puche was appointed assistant coach of Juan Carlos Mandiá in division two side Hércules CF. In the following years, the pair worked in several clubs.
Puche signed with Kuwaiti Premier League club Qadsia SC in 2014. He was sacked on 23 March of the following year, as the team went on to rank in fourth place.
Puche posted good scoring numbers with the Spanish under-16 team. In an international tournament held in Genoa, he was named as best player.
Puche also played at under-20 level, being selected for the squad that appeared at the 1989 FIFA World Youth Championship held in Saudi Arabia.
Puche's older, brother, José (1968), was also a footballer. A midfielder, he coincided with his sibling at Elche and Palamós, and the pair was known as Puche I and Puche II.Pichichi Trophy (Segunda División): 1994–95
AFC Cup: 2014
Kuwait Super Cup: 2014