My all time favorite jazz musician is Miles Davis. Anything from his album Kind of Blue is excellent, as well as Milestones or E.S.P.
However, the term "swing" refers to a style that is slightly less contemporary than artists like Miles Davis, with more of a big-band sound instead of be-bop. A great classic swing musician is Duke Ellington. Check out "Take the 'A' Train." Also check out Benny Goodman, Count Basie, Glen Miller, and Woody Herman.