...and like your tunes big, bold, and brassy...
- Count Basie is your man, especially his records from after 1950. His live album Count Basie at Newport has some great dance tunes at various tempos, and is also just awesome music. For mostly slower tempos, try April in Paris.
- Live in Swing City: Swingin' with the Duke by the Lincoln Center Jazz Orchestra is a reliable favorite. The disc contains modern renditions of classic tunes by Duke Ellington, making for interesting, dynamic, and playful music.
...and you like blues-influenced music with a lot of character...
- You can't beat Jimmie Witherspoon. Start with the compilation Jazz Me Blues.
- Check out Alberta Hunter's Amtrak Blues. It's got several songs that are between 100 and 150 beats per minute--nice slow, mostly chill music to practice your swingouts, with a beat that is easy to follow. Alberta Hunter was 80+ years old when she recorded this album, but her voice is still very spirited and memorable. This album also has "Darktown Strutter's Ball," which is a perpetual favorite among lindy hoppers--it starts off slow but then gets more energetic.
...and like stuff from the Rat Pack, Sinatra, Sammy Davis Jr., Dean Martin, Nat King Cole, that sort of thing...
- Check out the album With Respect to Nat by Oscar Peterson. Peterson is one of the most virtuosic jazz musicians of all time. He also does a dead-ringer impression of Nat King Cole on songs such as Walkin' My Baby Back Home and When My Sugar Walks Down the Street. The tempos on this album are mostly pretty slow, so you can lindy hop without breaking a sweat.
- You might dig Joe Williams, one of the most talented male singers in the history of jazz. Try the album One More for My Baby, where he is backed by a big, brassy orchestra, or the compilation The Definitive Joe Williams.
Note: Dancers, DJs, and folks searching for music, let me know what you think of these recommendations, and please don't be shy about posting a comment to suggest some of your favorites too.