The Beatles were known as The Quarrymen in 1958. Here's George, John, and Paul (no Ringo), performing "In Spite of All The Danger" on acoustic instruments.
Wikipedia has a good article about the song:
"In Spite of All the Danger" is one of the first songs recorded by The Quarrymen, then composed of John Lennon, Paul McCartney, George Harrison, pianist John Lowe and drummer Colin Hanton.
The song was written by McCartney and Harrison and is the only song to credit the two alone. It is believed to have been recorded on Saturday 12 July 1958 (three days before Lennon's mother's death). However, that recording date is disputed by the group. The recording was made at Percy Phillips' home studio in Liverpool (see 1958 in music), and cost 17 shillings and six pence (87.5p).
Here's Paul McCartney, many years later, talking about "In Spite of All The Danger" and performing it solo on guitar: