Get a microcontroller and a solderless breadboard. Play with them. You can do a lot with those two without having to be an electrical engineer; It can be tricky to get any sensor to work with a transistor (unless it's a transistor-type sensor, like a phototransistor). But with a microcontroller, turning any input into a meaningful output comes down to a little programming.

As far as at-home-building goes, you probably want the following tools:
- Power drill
- Hack saw
- Dremel
- Black sharpie
- T-Square ruler
- A few C-clamps
- A good set of adhesives. I recommend jb weld for plastics and metals, and gorilla glue for woods. It might be worth investing into hot glue as a temporary and quick adhesive, and some epoxy putty if you need a filler adhesive.
- If you're going to work with any screws or bolts in a vibration-heavy project, you probably want some loctite threadlocking adhesive.

With these tools, you should be able to do basic work with most woods and plastics.
It might also be worth getting a few files.

As far as electronic tools go, you probably want:
- Soldering Iron
- Wire Cutters/Strippers
- Heat Gun (this is also a great tool for working with acrylic)
- Multimeter

A DC power supply can also be very useful, but not mandatory.

Vibration music, where you repurpose some moving mechanism to emit your desired tones mostly involves a lot of your own software and a lot of experimenting. You pretty much have to experiment with whatever mechanism with various inputs (like various voltages for a dc motor) and figure out a trend line for input vs output tone. Once you have the trend line, it should be easy to write some software that can generate the desired tones with the mechanism.