Essentially your wanting a music and video server. There are many different video and audio servers available and at different price ranges and quality's.
It really depends on your budget, and convenient and easy the system is to use. It also depends if you really need to be able to burn blu rays as it requires special software and burners in order to do that.
I will talk about the best ones first and go down from there so you get the idea of what is possible and the price ranges you can spend.
Kaleidescape: Is still one of the best system out there, but it is very expensive. It has a great user interface, does allow you to burn your own blu ray disc's and music onto the system and access it from a really great interface.
Another option is building a custom video and music server using a personal computer. It must have a build in blu ray player and burner, with additional burning software purchased separately, You can use windows media center to access separate drives linked to the media center software. its a bit tricky to setup so you would need someone with some good PC knowledge. This can play blu rays and music.
Apple TV: Allows you to watch and play music and movies that you purchase on itunes. Very low price, good interface.
Kevin
40 years high end audio video specialist