Using an RC car as a robot base guarantees you that you'll have a decent base that's sturdy enough and suitable for your needs.
And since you want your robot to be RC, there's no question (imho) about it, use an existing RC car
Ofcourse buy one that can handly the terrain you want it to, and make sure it's not too crappy because you want it to be sturdy and powerfull enough to drag a sound system with it...
In what kind of environment do you want to play the music?
The speakers should be mounted on the robot right?
Maybe you can clarify howmany meters and feet 100 yards are.