Pardon the long delay.
For the NAS at that price, you are better off getting an all in one board with the CPU/GPU together which would run less than $100 USD which would easily fit your budget. This is a DIY build, so for the software you'd use for the "NAS" function, use FreeNAS. Since you aren't watching stuff on it, having an onboard GPU (powered by the CPU) would be just fine (aka non AMD or Nvidia GPU included with it).
Personally I have a QNAP 212 Turbo NAS which is about $200 USD (a few bucks more than your budget) and it comes all ready to go out of the box. Just add HDDs and configure from any computer on your network. It would be a TON easier to set up as everything you need is already there. If you can swing for it, I'd HIGHLY recommend that you get something like this. My personal one has 2x 3TB drives in JBOD and I love the thing to death
For the streaming PC (where you would be watching), keep in mind that the CPUs on the mini boards that you see on the market aren't capable that much of playing a large mkv (or other format) bluray file let alone any bluray disk. This is where having an Nvidia ION (or other GPU type) or an AMD HD card is best. Pick any board/CPU/GPU combination like I mentioned on this page for example: http://www.newegg.com/Store/SubCategory.aspx?SubCategory=446&name=Motherboard-CPU-VGA-Combo
. I realize this is newegg, but honestly I don't know what options you have where ever you live. I assume you are in the EU as you mention euro prices, so just try to match up something on that site like I suggested with what would fit your budget.
I can personally vouch for both nvidia ION and AMD's onboard GPUs (using an AMD APU netbook) and with the right software, you can offload the video processing to the GPU and have smooth sailing 1080p video.
For a media center experience, use XBMC (mandatory!). I spent probably a year and a half configuring codecs manually for the processing and then you had to worry about subtitles and other things going wrong like video/audio sync issues with other playback software. It was nasty! XBMC is the one to get. No fuss. Just set up your folders in it where it should find your media, either locally or on a network drive like I have. You can even combine folders from local and network drives to create 1 directory. I currently use this with my Atom 1.6ghz dual core/ION (GF 9400M) board combination.
If you don't want that experience, get VLC and in the options under Plugins and Codecs (I think that is what it is called from memory), enable the option for GPU processing. I'm using that set up currently with my AMD APU netbook and it can easily play any 1080p video I can throw at it at any size with CPU usage about 20% per core.
I hope all this helps. Again, pardon the delay. If you have any further questions, I set this thread to email me when you respond.Edited by NITRO1250 - 10/14/12 at 12:49pm