Personally I prefer a PC mainly for more usability and flexibility in upgrading them, and also "changing" the inside if you ever need it for other uses (or for better performance).
For the PC:
- Decent motherboard to ensure you can expand and add new HDD as needed (or cheap one)
- HDD with good cache and RPM (the standard ones are good, if you want to pay extra for the higher RPM HDD for faster read/write access, feel free)
- Low-end CPU is fine, streaming doesn't use all that much CPU power.
- 2GB+ of RAM is good :)
- A good network card to ensure it will handle the traffic
- Windows XP Pro is good (Simply creating share folders) - No need for Windows Server. My friend once recommended to use Linux as a file server, but since I have no hands-on experience on setting one as a network storage, I have no recommendations.
- Monitor + KB + Mouse is required only for initial set up (setting up user access, setting up folder shares, etc) but once its up and running, you can leave it monitorless and then control it using Remote Desktop (or VNC)
For the router, considering the size of the house, you might want to consider having 2 or more Wireless Routers to ensure you can cover the entirety of your house. (Currently using Linksys WRT54G (yes its an older model) and been a lot happy with it streaming movies from my main PC to play on my laptop).
Note: My current home set up is 1 PC, 1 router, 2 laptops, and its working perfectly fine streaming movies (both laptops streaming). If you have more users in the house that will be streaming and copying movies over the wireless, you might want to consider Wired solutions to ensure more stability.
I can't recommend any pricing, but I have heard stories from my friends who reused his old PC like an old Pentium 3, with 512MB RAM and used it as a network storage... but then again, I'm assuming he is using it purely for himself so that might not affect him all that much. So my current guess, its cheap :)
I hope this helps