The heart and soul of dancing comes from the music. The thrill, fun and joy of Lindy Hop comes from the diverse music styles that you are able do Lindy Hop movements to, in my opinion! Purists argue that executing Lindy Hop movements to music that is not from the swing era isn't Lindy Hop. I've "Lindyed" to AC/DC's Back in Black, Tom Jones' Sexbomb and OutKast's The Way You Move, so to me it's not an argument worth having, afterall it's all about having a good time.
Whether it's dancing to heart-pumping songs like Benny Goodman's Sing, Sing, Sing and Louis Jordan's Beans and Cornbread or the gentle crooning in Ella Fitzgerald's Smooth Sailing to Bobby Darrin's Beyond The Sea, music tempos play a huge factor in enjoyment, too. The more you dance, the more familiar you become with the subtle nuances of each song. You develop your musicality and the ability to "play" with the melodies and instruments and do movements to enhance what you and your partner create.
I strongly recommend that new dancers "cut their teeth" to moderate tempos, for the first couple of months, as you need to have an good understanding of the concepts of Frame and Connection before tackling the faster and slower songs.
Here's a sampling of songs I enjoy. The song in red have faster tempos, while those in blue are slower, some leaning towards bluesy tunes. If you're interested in accquiring any of these songs, please consider using the iTunes link 
next to the title. The songs, through Apple's iTunes Music Store, are only 99 cents and a purchase here earn me a modest commission. When you click the link, iTunes (if installed) will (eventually/slowly) open and take you directly to the song, where you can hear a 30-second sample of the song.. If you don't have iTunes installed a window will open and take you to the FREE download of iTunes, and then you need to come back here and select your song.
- Beyond the Sea by Bobby Darin
- When The Lights Go Out by Jimmy Witherspoon
- My Baby Just Cares for Me by Nina Simone
- Easy Does It by Count Basie
- They Can't Take That Away From Me by Ella Fitzgerald & Louis Armstrong
- Out South by The Duke Ellington Small Bands
- Regular Joe by Indigo Swing
- Good Queen Bess (Live) by Johnny Hodges
- Every Day I Have The Blues by Joe Williams
- Shiny Stockings by Count Basie
- Smooth Sailing by Ella Fitzgerald
- Four or Five Times by Joe Williams
- Blues For Stephanie by George Gee
- Corner Pocket (aka Until I Met You) by Duke Ellington
- Stompin' At The Savoy by Nina Simone
- Moondance by Barbara Folden - Michael Raphael
- 9:20 Special by Count Basie
- Bei Mir Bist Du Schoen by Ella Fitzgerald
- One Mint Julep by Count Basie Orch.
- Our Love Is Here To Stay by Blossom Dearie
- Ruby Mae by Indigo Swing
- Nobody But Me by Lou Rawls
- For Dancers Only by Duke Ellington
- Teardrops From My Eyes by Ruth Brown
- Frankie and Johnny by Sam Cooke
- At Last! by Etta James
- Sympathique by Caroline Moreau
- Lavender Coffin by Lionel Hampton
- 13 Step Boogie by Martin Sexton
- Hello Dolly by Louis Armstrong
- Mack the Knife by Ella Fitzgerald
- I'd Rather Drink Muddy Water by Lou Rawls
- Knock Me a Kiss by Louis Jordan and his Tympany Five
- Today's the Day I'm Glad I'm Not Dead by Indigo Swing
- Splanky by Count Basie
- A Natural Man by Lou Rawls
- Shake, Rattle And Roll by Sam Cooke
- Blue Skies by Ella Fitzgerald
- Ain't Nobody Here But Us Chickens by Louis Jordan and his Tympany Five
- Beans and Cornbread by Louis Jordan and his Tympany Five
- Doop-Doo-De-Doop-A Doodlin' Song by Blossom Dearie
- Fever by Peggy Lee
- Fire by Des'ree / Babyface
- Sexbomb by Tom Jones
- G.I. Jive by Louis Jordan and his Tympany Five
- Wake Up Neesie by Kermit Ruffins
- A Smooth One by Junior Mance
- Duke's Place by Ella Fitzgerald
- Exactly Like You by Carmen Mcrae
- Summertime by Chris Connor
- Times Gettin' Tougher Than Tough by Jimmy Witherspoon
- Bill Bailey, Won't You Please Come Home? by Ella Fitzgerald
- Kansas City Riffs by Buster Smith
- Rockhouse (Parts 1 And 2) by Ray Charles
- The Way You Move by Outkast
- Lucas With The Lid Off by Lucas
- Green Onions by Booker T & the MGs
- Jacquet In The Box by Jonathan Stout & his Campus Five
- Dance With Me by Debelah Morgan
- Is You Is or Is You Ain't (My Baby) by Louis Jordan
- Moten Swing by Count Basie
- Let's Call the Whole Thing Off by Ella Fitzgerald & Louis Armstrong
- Why Don't You Do Right by Benny Goodman & His Orchestra
- Cheek to Cheek by Ella Fitzgerald & Louis Armstrong
- Surrey With The Fringe On Top by Mary Stallings
- Streamliner by Bill Elliott Swing Orchestra
- Blue Suit Boogie by Indigo Swing
- Money's Gettin' Cheaper by Jimmy Witherspoon
- Choo Choo Ch'boogie by Louis Jordan & His Tympany Five
- You Are My Sunshine by Gene Harris/Scott Hamilton Quintet
- A Smooth One by Junior Mance
- Sugar In My Bowl by Nina Simone
- Can't Stop Thinking Bout You by Martin Sexton
- Summertime by Gene Harris Quartet
- Lonely Avenue by Ray Charles
- Peel Me A Grape by Diana Krall
- Just My Imagination by The Temptations
- Temptation by Diana Krall
- Bits and Pieces by Clarence Gatemouth Brown
- Mary by Take 6
- M!ssundaztood by Pink
- Down By The River Side by the Benny Green Trio
- Groove Me by King Floyd