Bass triggered lights

I am interested in making a small circuit that can flash a set of LEDs along with music.
I have no idea how to go about this but so far my idea is:

Take music input (1/8" jack or something) --> Low Pass Filter --> Transistor or some amplification --> Triggers a solid state relay to switch LEDs on and off.

Am I on the right track?

You're on the right track.

I'd say something more like input--> low-pass filter--> amplification stage--> BJT or MOSFET transistor to control LEDs. You don't need a SSR here.

Op amps would probably be easiest way to implement 1 & 2 (filter + amplification). Since you're dealing with low frequency here (<1kHz), almost any old op amp will do.

Its called a color organ.