Which Arduino board should I use?

garrampa:
Can I use an Arduino 101/ Genuino 101 with Bluetooth integrated so I can avoid the Bluetooth module?

I believe the 101 has an onboard BLE, so yes.
You should need no more than the LED and a resistor, about 560 Ohm. I don't think this merits a breadboard, but those tiny ones about 12 holes square are only about 50c.