I recently built a HTPC ..... a large part of the cost was the case I chose, because I wanted it to sit under the TV.
Another large part of the cost was my decision to only accept a motherboard with both SATA III and USB 3.
Also, I paid a high price for a PCI-e Satellite card with dual tuners, so one could be used to record a channel while watching another channel on a different transponder. I also have a cheap (~$20) USB dongle for DTT.
If those three above are not important to you then the cost can be low.
As I write I am using Kaffeine on PCLOS in the box because it does the LiveTV very well.
I expect to change to XBMC as soon as the latest version is released ....... it includes LiveTV functionality whereas the existing XBMC in the repo does not.
So, as you can see most of my emphasis has been on LiveTV, which has upped the cost a lot.
The benefit for me is that the HTPC can be used as a normal PC outputting to the TV, with all that entails.
I have also been trialling Openelec with the newer XBMC and it too does LiveTV as well as PVR, runs 'live' with persistence, and has a footprint of less than 200MB presently.
There are different OS images for different hardware.
If versatility is important to you then I strongly suggest a micro/miniATX motherboard etc.
The other alternative is to use something like the Raspberry Pi as a front end to a server/backend box.
I do not believe the R-Pi is a cost effective solution for this.
You get a bare board to which you need to add
Power supply 5V 1.5A minimum
SDHC card class 4 minimum, class 10 recommended, of 4GB minimum in size
Case ... cannot really leave the bare board hanging about
Also note, as there is no on/off power switch on the Pi some other scheme for turning it off will be needed.
NAS boxes are quite dear for what you get .... most without disks, and very limited in number of disks and how they are set up. Also the control firmware can limit some things you might wish to have.
So, from my personal perspective, a good case with room for a few disks, running a full version of Linux with all the applications and packages available from the repositories, gives the functionality I want now and room to change as my needs change, without changing the hardware.
One thing I would emphasise ..... if the HTPC is to sit in the living room then you need as 'near silent' a build as possible.
It is quite possible that there are now available multicore, fanless designs of motherboard that would suit.
I chose a motherboard with CPU socket, so that if I need to upgrade the CPU in the future I can.
The only time I hear the fans is on power on ... when they spin at full speed for a few seconds.
After that you need to be next to the HTPC, with the TV sound muted, to hear any noise.
There are a few threads on the forum which should be of interest. This is one I started when going through the processhttp://www.pclinuxos.com/forum/index.php/topic,109221.0.html
Good luck with whichever route you take!
I have lots of links on the subject .... here's a fewhttp://www.avsforum.com/f/http://forum.xbmc.org/forumdisplay.php?fid=112http://openelec.tv/
as well as other more specific links ...http://zotac.com/http://tinyurl.com/b23s3k8