Strike up the band for ''My One and Only.'' After all of its widely reported trials and tribulations, this ''new Gershwin musical'' turns out to be a sweet and funny show with a fine old Gershwin score, a daffy but genial book, lots of wonderful tap-dancing, and two stars - Twiggy and Tommy Tune - who give a new meaning to apt alliteration.
The airy romance concocted by Peter Stone and Timothy S. Mayer recalls the cloud-cuckoo land that Broadway musicals used regularly to inhabit. The plot concerns Capt. Billy Buck Chandler (Mr. Tune), a hayseed Texas pilot bent on becoming the first American to fly New York to Paris nonstop, and Edith Herbert (Twiggy), a British channel swimmer visiting the United States as the star of an aquacade. Temporarily foiled in his pursuit of Edith by her rascally Russian manager (Bruce McGill), Billy rises above every obstacle as the authors navigate their way to a happy ending.
Meanwhile, the collaborators are helping themselves liberally to goodies from the copious Gershwin song bag. They have retained five numbers from ''Funny Face ,'' the 1927 musical that inspired ''My One and Only.'' Various Gershwin stage and film musicals of the '20s and '30s plus some heretofore un-heard material - smartly orchestrated by Michael Gibson - contribute to the pleasures of the lilting entertainment at the St. James Theatre.
The two melodic highlights of act one are ''He Loves and She Loves,'' sung by Mr. Tune and Twiggy as they watch a steamy Valentino-type movie, and '''S Wonderful,'' with which the lovers discover their mutual devotion while stranded on an exotic isle that turns out to be Staten Island. Before being rescued by the Staten Island ferry, they splash about barefoot in an enchanting shallow-water number that stops the show.
''Nice Work If You Can Get It'' is here concerned with Edith's aquacade career, while Mr. Tune and the great Charles ''Honi'' Coles set things soaring with their song-and-tap performance of the title number. Mr. Coles plays Mr. Magix, a Harlem barbershop counselor on matters of haberdashery and the heart. Needless to say, he spreads magic wherever he goes.
''Strike Up the Band,'' the title song of yet another Gershwin show, climaxes both the first and second acts of ''My One and Only'' in splendid style. Among the other numbers with which Mr. Tune and codirector-choreographer Thommie Walsh celebrate their Gershwin festival are ''Blah, Blah, Blah,'' ''I Can't Be Bothered Now'' (sung by the New Rhythm Boys), ''Just Another Rhumba'' (sung by the inimitable Roscoe Lee Browne), ''How Long Has This Been Goin' On'' (by Twiggy and Mr. Tune), and ''Funny Face'' (Mr. McGill in duet with perky Denny Dillon).
''My One and Only'' is happy in its starring twosome. Twiggy is slight, graceful, and adorable, with a reedy but pleasing voice and a gift for comedy. (Is anyone thinking of her for a musical about Gertrude Lawrence?) Mr. Tune proves once more a trouper as talented as he is tall (six foot six). Whether singing or tapping or clowning around, he is a joy to watch, and he shares his relish of the infectious Gershwin material.
Taking it altogether, ''My One and Only'' is a skylarking entertainment. The collaborators have entered into the spirit of a dizzy earlier period and recreated it in their own style with fun and affection. Wicked ''Prince'' Nikki's aquacade troupe pays tribute to the chorines who populated shows patronized by yesteryear's tired businessmen. Besides the tone-setting New Rhythm Boys, there is a fine ensemble of black singer-dancers, the Dancing Gentlemen, and a white singing foursome known as the Ritz Quartette.
The designs are antic, eye catching, and bathed in bright colors. The program credits Adrianne Lobel (scenery), Rita Ryack (costumes), Marcia Madeira (lighting), and Otts Munderloh (sound). Among the vital creative contributions are those of Wally Harper, for musical concept and dance arrangements; Peter Larson, for dance arrangements; and Jack Lee, the musical and vocal director.