what are the different ways to set up a stereo music system at home?

There are a few parameters / criteria that you will have to think through:
1. Where will this be located
2. Would you want to share it with others or have a personal listening session
3. Would your stereo setup play a dual role as part of your Home Theater system
4. How large is the space
6. What is your budget

There are different components to a music system 
1. Music source - Streaming (e.g. Spotify), CD, LP record player
2. Digital to Analog converter (DAC)
3. Preamplifier - Required for volume control and if you have multiple sources
4. Stereo Amplifier
5. Speakers or Headphones
    -- Speakers - Can be bookshelf speakers (for small spaces) or floorstanding speakers (for large spaces)
    -- Headphones - Can be open back (great for quiet places and no other people around who may get disturbed) or closed back (noisy environment or other people present). You will also need to think through if you want noise cancellation or not (usage on flights etc will require a closed back headphone with Active Noise Cancellation)