Single time swing would be the easiest dance to learn. Up tempo 60's music is a form of swing and some ballroom DJs, play a lot of 60's music. Many of the 60's hits are remakes of 40's swing music. Once you learn single time, learning East coast would be a good next choice. Since you can use same manuevers, replacing the 2 slows with 2 triple steps.

A minority opinion is that 60's music is the best swing music. I don't agree with that, but still think it is good swing music and fun to dance to.