1. HDMI: *Recommended*
HDMI cables are an all-in-one solution designed to transfer both audio and video. The HDMI cable is also the most advanced as it's able to deliver uncompressed audio to 8 channels for a full 7.1 speaker experience (in popular Dolby TrueHD and DTS HD formats likely used by a Blu-Ray disk). The HDMI Cable also can handle 3D and 4K content, making it a future-proof choice when piecing together your home theater.
2. Optical / Toslink:
As HDMI cables have become cheaper and more prominent, optical cables have started becoming a less common choice. Optical cables work by transmitting light pulses through a hollow channel in the middle of the wire. This makes the cable a great solution with minimal signal degradation, but it is also limited to transferring only up to 5.1 surround sound.
3. Digital Coaxial:
Digital coaxial cables are very common and can deliver 5.1 surround sound audio, just like an Optical or Toslink cable. They are typically used to connect a subwoofer to an audio receiver, and the difference in sound quality between a digital coaxial and a optical cable are nearly indistinguishable.
These are the cables your parent's likely used. They're analog, but are able to provide surround sound with multiple connections. Given that they were originally designed to transfer analog sound, they can degrade the sound quality of digital recordings. For that reason, you'll likely move past these cables and onto one of the options listed above.