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!
Squeezebox would work great for the application you have in mind. They work completely wirelessly other than your coax or toslink connection to your DAC. You shouldn't have to move any of your other equipment in order to make the interface possible.
Bearotti , Thanks, so I can leave the External Hard drive upstairs and use my Laptop in the basement?
Any particular Squeezebox would you reccomend?
Sonos would be an even better choice. Much more turnkey, better user interface. No need to become a computer geek, and Sonos has maybe the best customer service I've ever experienced. Also the Sonos with a NAS drive is designed so that your computer need not even be on. I'd peruse the Sonos web site a bit.
So if I buy the Squeezebox Touch and connect it to my Audio systems Dac with a Coaxial digital cable , how does the music from my external hardrive send the signal to the Squeezebox touch???
Via your network.. all the answers are here http://www.logitech.com/en-us/speakers_audio/wireless_music_systems/devices/5745