Laura Hopkins' set designs for Annie Get Your Gun range freely from Death Valley (or somewhere similar) to a cattle boat crossing the Atlantic to a New York hotel ballroom, but always they leave plenty of room on the vast Crucible stage for director Paul Foster to fill: with the spectacle of Buffalo Bill's Wild West show, perhaps, or Alistair David's vivid choreography or simply with Anna-Jane Casey's irrepressible and effervescent Annie Oakley.

Foster's thoroughly professional production of Irving Berlin's classic musical is lifted by two outstanding performances at its core, from Casey and Ben Lewis as Frank Butler. The competitive love story of these two champion sharpshooters provides much of the plot, together with the successes and financial problems of Buffalo Bill and his show. Dorothy and Herbert Fields' book, revised by Peter Stone, abounds in comic or spectacular set pieces just as Berlin's score abounds in wonderful songs, though some may miss "I'm an Indian Too", just too full of mid-20th century attitudes to Native Americans for a 21st century audience. Chief Sitting Bull himself is wisely sympathetic in Karl Seth's nicely judged performance.

Perhaps Annie Get Your Gun is too front-loaded with great songs. Where do you go after the perpetually rewarding and infinitely adaptable anthem, "There's No Business Like Show Business", the sweetly teasing love duet "The Girl That I Marry" and Annie's two bits of backwoods philosophy, "Doin' What Comes Natur'lly" and "You Can't Get a Man with a Gun", which Casey delivers with a feral mischief reminiscent of the great Betty Hutton? There are plenty more good songs, some smart or moving dialogue scenes, but the thrill of seeing and hearing something special returns only with Casey ripping virtuosic strips off "Anything You Can Do", with Lewis in witty and melodious support.

Foster's production is strongly cast, with reliable performances and good singing voices all down the line. Nicolas Colicos has the benign eccentricity needed for Buffalo Bill; Timothy Quinlan complements him neatly as his canny business adviser Charlie Davenport; as the "second couple", Winnie and Tommy, Lauren Hall and Cleve September dance up a storm on one of Berlin's less memorable numbers, "Who Do You Love"; and Maggie Service projects malice and jealousy in equal quantity as Dolly Tate until reduced to hilarious gibbering by the thought that someone finds her exciting.

This is a large-scale production, with opulent and imaginative costumes, a 12-piece band under Paul Herbert and 23 named performers, plus three talented and confident children, but always you come back to Anna-Jane Casey and Ben Lewis. He starts the evening arrestingly with an immaculate a cappella verse of "There's No Business" from the back of the stalls and exudes a gentlemanly polish throughout even when his vanity is piqued. She changes scene by scene, her songs varying from backwoods comedy to romantic sincerity to Ethel Merman-style brassiness. Both are unfailingly human and likeable.

Click here to read our interview with Anna-Jane Casey

Annie Get Your Gun runs at the Sheffield Crucible until 21 January 2017.