Staunton was raised in Carnacon, County Mayo. Her father was a farmer and her mother worked in the catering department of a local hospital. She has four brothers and three sisters and is the second youngest amongst her siblings. In 1995, her mother, Mary, was diagnosed with cancer. She died on 11 July 1998 when Staunton was 16.
Gaelic football
Staunton began playing Gaelic football at the age of seven in her local school in Carnacon. She later played with boys' teams in nearby Ballinrobe. Among her earliest team mates was Alan Dillon. Staunton made her debut for the Mayo senior ladies' football team in 1995 aged just 13. She made her first appearance in an All-Ireland final in 1999. However, she played just 90 seconds of the game because she had broken her collarbone in training a week before the final. The team elected to start her anyway, as a ceremonial gesture. She made her second All-Ireland appearance in 2000, scoring 2:2 as Mayo defeated Waterford. Staunton's third All-Ireland appearance in 2001 ended in disappointment after a mix-up over a last minute kick-out saw Mayo lose by a single point to Laois. However Staunton and Mayo then won two successive All-Irelands in 2002 and 2003. Staunton played in a sixth All-Ireland in 2007. Staunton has also won six All-Ireland Ladies Club Football Championships with her club, Carnacon.
Association football
Staunton plays association football for Ballyglass Ladies in the Mayo Ladies League. As a youth she was invited to trials for the Republic of Ireland U–16s but she declined, preferring to concentrate on Gaelic football. However, she continued to play association football at club level. In 2006, she was a member of the Mayo Ladies League representative team that won the FAI Women's Cup, defeating UCD 1–0 in the final at Richmond Park. Staunton was just one of several members of the Mayo Ladies League representative team who also played Ladies Gaelic football for Mayo. Others included Yvonne Byrne, Aoife Herbert, Michelle Ruane, Martha Carter, Triona McNicholas and Emma Mullin. As a result of winning the 2006 FAI Women's Cup, the Mayo Ladies League qualified to represent the Republic of Ireland in the 2007–08 UEFA Women's Cup. The competition format saw the team travel to Austria in August 2007 to play in a mini-tournament to decide who would progress to the next round. Unfortunately the UEFA Women's Cup tournament clashed with a 2007 All-Ireland Senior Ladies' Football Championship quarter-final game against Monaghan. In the opening game of the tournament, Staunton scored for Mayo in a 4–1 defeat to Gol Częstochowa. However, she then returned to Ireland, along with Yvonne Byrne and Aoife Herbert, to line-up against Monaghan. While playing with Ballyglass Ladies, Staunton also won the 2011 WFAI Intermediate Cup.
In September 2013 Staunton made her rugby union debut for Castlebar Ladies in a Connacht Women's League game against Tuam. She subsequently scored seven tries in a 68–15 win. She also went onto captain Castlebar to the league title.