Wireless Connection from Xternal HD to Stereo

I am fairly new to the world of wireless PC features. Perhaps because I am 57 years old and I have never had too much exposure to it.
I know how to use Word, Excel, PowerPoint, the internet etc. But, I don’t know much about external PC devices. The "youts" at BB are not much help.

I recently bought a new Laptop and a 1 TB external hard drive to transfer primarily music via Apple Lossless mode.
I have a wireless router along with the 1 TB External Hard Drive that is located in the upper level.
My stereo system is in the basement. I am able to access the internet via the wireless Router with my Laptop in the basement.

So, here is my main question...

I want to be able to play songs from my external hard drive to my Stereo. I imagine a device that can be plugged into my Laptop (via a USB) that wirelessly sends the sound to my Stereo using some sort of receiver.
The output of the Receiver should be digital, either Coaxial or Toslink.

Remember though, my external Hard Drive is in the upper level of my home along with the wireless router.
If this proves to be too much hassle I suppose I could place the External Hard Dive in the basement, but the Router would remain in the upper level.

I have heard about units such as a Squeezebox but I have no idea how they work and if they would work with the setup I have described.

So what is suggested? Please provide me some direction, thanks!