As it is likely known to any good Beatles fan (that is, anyone who has bought Anthology 1), The Beatles, still known as The Quarrymen but now including Paul and George, recorded in a studio for the first time in 1958. "That'll Be the Day" is one of two songs they recorded.
"That'll Be the Day" wasn't Buddy Holly's first professional recording by far, nor was it the first released, but it was his first hit, and it made him a huge star on both sides of the Atlantic. Buddy Holly's earliest recordings are pure country, moving on to pure rockabilly, but 1957 seems to be when he found his own unique voice and style, which I personally describe as a crossover from rockabilly to straightforward rock 'n' roll. Buddy Holly's creativity and incredibly diverse use of little more than three chords in the key of A made him an innovator, and likely the first singer-songwriter of rock 'n' roll.
Buddy Holly's music had a tremendous influence on The Beatles, and they would perform and record several more of his songs throughout their careers. John emulated his style in his early days, often wearing glasses like his, and an early version of his song "Hello Little Girl" clearly shows his influence. Heck, Paul even bought his song catalogue not too long ago!
The Quarrymen version of "That'll Be the Day" is pretty much a straight copy of the original, showing that they could learn songs better than they used to. I read once that they once thought that all of his songs were in the key of C, rather than A, and played them like that for a while- but that doesn't seem to be the case here.
Anyway, if "Baby, Let's Play House" wasn't rock 'n' roll enough for you, perhaps this song is. Even so, there are some that are even more rock 'n' roll than this...
So now we've got skiffle, rockabilly, and rock 'n' roll. Obviously, it'll diversify later.