I'm not saying you should have no experience in these styles. I just personally would never program a work from the Baroque or Classical period on a recital. Bach I would do on a church program, but why not use something like the Guy de Lioncourt, "Trois Medlodies Greogriennes"? These are beautiful works for alto saxophone and organ/piano and they are perfect for a church service, in a baroque style, and are also original works for saxophone.
As far as being missionaries for the saxophone, I've never won any converts playing transcriptions. The most enthusiastic responses to my playing have always come from people excited about the original repertoire they heard at a concert or recital. It requires careful planning to create a program of pieces accessible to the audience and still musically solid, but I've found it's well worth it.
So pieces I'd suggest every saxophonist should own would include:
Concertos:
Glazunov, Ibert, Milhaud, Debussy, D'Indy, Martin, Larsson, Von-Koch, Dahl, Husa, Maurice, Tomasi.
Concert-Pieces:
Albright Sonata
Yoshimatsu, Fuzzy Bird Sonata
Harbison, San Antonio
Zwilich, Episodes
Heiden, Sonata
Denisov, Sonata
Creston, Sonata
Desenclos, Prelude, Cadence, and Finale
Bolcom, Lilith
Chamber Music:
Webern, Op.22
Laitman, I Never Saw Another Butterfly
Hindemith, Trio
Eychenne, Cantilene and Danse
Denisov, Sonate for Alto Saxophone and Cello
Hartley, Lyric Suite