Powering light/music system

Would it be feasible to wire a switch to an Arduino that, when engaged, engages another switch giving power to a lighting system, as well as wirelessly send a message to a computer (via bluetooth) to play a specific song? Any help/comments/advice would be much appreciated

Yes, very possible.

Giving power to the lighting system will need a big relay capable of handling the voltage and current requirements of the lighting system. You will probably need to use a MOSFET (an electronic switch) to drive the coil of that relay.

Bluetooth can be added with a simple Bluetooth module that is made to send serial data to the computer. Once you have the message to the computer there are many ways to play the music. I personally would write a short python program that connects to the serial port and waits for the command, and when it receives it plays the song, but I wouldn't be surprised if someone hear knows an even simpler way.

Thanks a lot! I'll try to piece together the materials in the next week and get started. Have a good one