Impossible for me to name a favourite from so many. All have their own sound and bring their own goodies to the music player.
When I caught the jazz bug way back it was Bill Harris who hit the spot (a sort of blasting, bleating, stuttering hectoring style with Woody and when burning it up on a JATP jam) then I thought best to check back in time and hear what had went before. I then dug J C Higganbotham, then Jack Teagarden, and of course Dicky Wells (who was with Basie) who recorded classic sides in Paris (1937). Then the laid back style of Vic Dickenson, be bopping with J J Johnson, and Kai Winding, while then digesting the guys who were busting through in the fifties,Frank Rosolino, Carl Fontana, Jimmy Cleveland, Curtis Fuller, valve trombonists Bob Brookmeyer, Bob Enevoldsen, and (with Basie and Duke) Lawrence Brown, Quentin Jackson, Al Grey. Also Roy Williams (UK) James Morrison (Australia, multi instrumentalist), Al Mangelsdorff (mainstream, avant garde and various styles, Germany), Glenn Ferris (USA, moved to France in 1980, recorded with numerous big names)...just some of the many who make me sit up and take notice.