Born in St Asaph, Denbighshire , Rush's reputation was enhanced by scoring for Chester City in a shock 2–0 FA Cup third round win at Second Division side Newcastle United in January 1980, with Chester City equalling their best run by reaching the last 16 where they narrowly lost to Ipswich Town. His last game for Chester City was a 2–1 win over Southend United at Sealand Road on 26 April 1980 in which he did not score.
Despite interest from Manchester City, and in spite of Rush being a boyhood Everton fan, Liverpool won the race to sign the 18-year-old in April 1980, though he had to remain at Chester until the end of the season as the transfer deadline (27 March 1980) had passed. Recommended by chief scout Geoff Twentyman, Liverpool paid a record fee for a teenager of £300,000. It remained Chester City's record sale until they went bankrupt in March 2010. Rush was managed throughout his time at Chester by Alan Oakes, although much of the credit for his development is given to youth manager Cliff Sear. Nearly 20 years later, Rush and Sear worked together on the coaching staff at Wrexham.
Rush made his international début, in May 1980, just before he officially became a Liverpool player. His Reds début came on 13 December that year in a First Division fixture at Portman Road against Ipswich Town. He was standing in for his future strike-partner, Kenny Dalglish (out with an ankle injury but at the time one of the most highly rated strikers in the world), and wore his No 7 shirt. At this stage, Liverpool were defending the league title and the League Cup, and also contending for the European Cup, while Ipswich were emerging as surprise title contenders. Liverpool finished fifth (with Aston Villa winning the title), but they did win the European Cup (for the third time) and the League Cup (for the first time).
Rush made his Welsh debut before he had been handed his first start for Liverpool, playing his first match on 21 May 1980 against Scotland in Glasgow, a 0–1 loss. He played his last international match on 24 January 1996 – a friendly match against Italy in Terni which Wales lost 0–3. Rush played regularly for the Welsh national team for more than 15 years, scoring 28 goals in 73 games.