As an oboist he recorded more than 20 solo and recital compact discs as well as recording frequently with leading London "original instrument" Baroque ensembles. Among those discs are an acclaimed set of Vivaldi oboe sonatas, another of seven Vivaldi concertos with oboe, and oboe sonatas of Georg Philip Telemann.

In addition to playing in major venues and festivals around the world, Goodwin also became well known for his teaching and his work with student musicians.

After he began conducting, Goodwin received major recognition when Christopher Hogwood, founder and conductor of the Academy of Ancient Music, appointed him associate conductor of the academy. His skills with standard instrument ensembles were also obvious, and he became principal guest conductor of the English Chamber Orchestra. He has guest conducted major orchestras of all sizes, both standard instruments and period instruments. These include the Saint Paul Chamber Orchestra, the Swedish Chamber Orchestra, the Zurich Chamber Orchestra, the Orchestre National de Lille, the Ulster Orchestra, the Camerata Academica Salzburg, and the City of Birmingham Symphony Orchestra. He is also a sensitive choral conductor who has led the Belfast Philharmonic Choir, the RIAS Kammerchor Berlin, and the Tallis Chamber Choir and been invited to take the Netherlands Chamber Choir on tour. As a conductor, Goodwin is an exclusive Harmonia Mundi USA recording artist, including his performances with the Academy of Ancient Music. Notable projects with the AAM has included tours devoted to the music of Monteverdi and Schütz and Mozart's almost unknown Singspiel Zaïde. In 1999, Goodwin made his BBC Proms Concerts conducting debut with the academy in a program of Handel, Haydn, and contemporary composer John Tavener.

The European interest in reviving Baroque-era opera has shown Goodwin to be a dramatic and effective theater conductor. He conducted Jonathan Miller's acclaimed and innovative staging of Bach's St. Matthew Passion as well as Handel's Agrippina, Amadigi, and Poro, Monteverdi's L'incoronazione di Poppea, and Classical-era works including Gluck's Orfeo and Haydn's L'isola disabitata, as well as Mozart's Marriage of Figaro and Il rè pastore.

Goodwin is highly interested in the idea of promoting contemporary composers to write for Baroque-period instruments. This has resulted in commissions from British composer John Tavener, whose Eternity's Sunrise was the first work commissioned by Goodwin for the academy, and who has gone on to write the large-scale cantata Total Eclipse. David Bedford has also agreed to write an orchestral suite for the academy.

Goodwin continues his interest in music education and youth orchestras. He often works with the Baroque and Classical orchestras of the Royal Academy of Music and the Royal College of Music in London. He is director of the Dartington International Summer School Baroque Orchestra and Early Opera and has worked with the Spanish Youth Orchestra (JONDE), the Britten-Pears Orchestra, the European Community Baroque Orchestra, and the Jeune Orchestre Atlantique.