First of all, Buddy Holly's band, the Crickets, inspired the Beatles own insectoid name.
Quoting Paul McCartney: "I remember talking to John about this. 'Cricket. What a fantastic idea, it's a little grasshopper, and it's a game.' Well, they came over, they had no fucking idea cricket was a game, to them it was just a little chirping grasshopper from Texas, so it was actually quite a boring name. But we were turned on like nobody's business by the idea of a double meaning, so with our wit and wisdom and whatever, we wanted something that would have a double meaning. Beetles were little insects, so that took care of that, but with an 'A' it became something to do with beat" (Miles, page 52). Lennon confirms this: "I was looking for a name like The Crickets that meant two things, and from crickets I got to beetles. And I changed the BEA, because 'beetles' didn't mean two things on its own. When you said it, people thought of crawly things; and when you read it, it was beat music" (Anthology, page 41).
Second, it was Buddy Holly who inspired John Lennon and Paul McCartney to play, sing, and write their own songs. Quoting John Lennon: "Buddy Holly was the first one that we were really aware of in England who could play and sing at the same time - not just strum, but actually play the licks" (Anthology, page 11). It is a safe bet to assume that Lennon is referring to Elvis Presley, who was a major influence, but was more of a singer than a guitar player. (I've heard Presley occasionally described that "he wore the guitar better than he played it".) Holly, by contrast, could do both simultaneously. More importantly, Holly wrote original material, further inspiring the Beatles to do likewise. Quoting Paul once more: "I still like Buddy's vocal style. And his writing. One of the main things about The Beatles is that we started out writing our own material. People these days take it for granted that you do, but nobody used to then. John I started to write because of Buddy Holly. It was like, 'Wow! He writes and is a musician'" (Anthology, page 22).
Eventually, of course, the Beatles would write, perform, and record almost exclusively only original material. But in the early years, the band's repertoire leaned heavily on cover songs for the majority of their stage repertoire. And throughout the Quarrymen/Beatles' existence, they played a total of at least 13 Buddy Holly songs in live shows (as dictated in Lewisohn, page 362-65).
- "Baby I Don't Care (You're So Square)", 1960-61
- "Crying, Waiting, Hoping", 1960-62
- "Everyday", 1957-62
- "It's So Easy", 1958-62
- "Mailman, Bring Me No More Blues", 1961-62
- "Maybe Baby", 1958-61
- "Midnight Shift", 1960-62
- "Peggy Sue", 1957-62
- "Raining in My Heart", 1959-62
- "Reminiscing", 1962-63
- "That'll Be the Day", 1957-60
- "Think it Over", 1958-62
- "Words of Love", 1958-62
Recordings of the Beatles' performances of these Buddy Holly songs exist for only 6 of the 13 listed above.
The first professional recording the Beatles (then the Quarrymen) ever made was their rendition of "That'll Be The Day", recorded 12(?) July 1958, but not commercially released until The Beatles Anthology 1.
Beatles, The. The Beatles Anthology. Chronicle Books, San Francisco, CA, 2000.
Lewisohn, Mark. The Complete Beatles Chronicle. Pyramid Books, an imprint of Octopus Publishing Group Limited, London, UK, 2006.
Miles, Barry. Paul McCartney: Many Years From Now. Henry Holt and Company, New York, NY, 1997.