The best music in the 60's was from Motown, Atlantic Records or the Beach music from people like Jan & Dean or The Beach Boys. Stevie Wonder, The Supremes and Smokey Robinson and the other Motown stars dominated the charts.
The best artist from the 1960s would have to be The Beatles. There are many close behind, though, including The Rolling Stones, The Who, The Animals, and Bob Dylan. Don't forget Elvis Presley either.