Depending on your Linux distribution, you should generally be able to get good stability and performance out of Intel Sandy Bridge graphics (at least for the purposes of a HTPC).
About a year ago, I rebuilt my HTPC, which is Linux + MythTV based. At the time, useful Linux SNB GPU drivers were not yet mainstream ready, so I put a GT430 in my system.
However, since roughly January this year, I've removed the nVidia card, and am happily using the Intel GPU exclusively. My CPU is an i3-2100. This CPU has been powerful enough for
software based decoding of HD Bluray content; at least the content I've thrown at it. Not all HD/Bluray content is created equal. But I ran across
this thread on the MythTV mailing list. To summarize, someone is talking about how a particular bluray (Transformers 2) is encoded with a single slice for the first three chapters and that software-decoding on a Core i7 920 (2.6 Ghz) is choppy. I have this Bluray and it plays perfectly on my i3-2100. Note that the MythTV post was from Nov, 2009. I've got a faster-clocked CPU (with a better architecture), plus I assume the software has improved as well. But note that my i3-2100 is pegged at 100% CPU when this Bluray is playing.
Just for fun, this weekend, I compiled mplayer with VA-API support (vaapi is basically the equivalent of vdpau for Intel and AMD GPUs). With mplayer-vaapi, playing this same Bluray resulted in a CPU load that never went above 5%. Version 0.25 of MythTV was recently released; one of the many new features is built-in VA-API support. I haven't upgraded yet (still on 0.24), which means I don't have vaapi support... but everything works perfectly as-is, so I see no reason to risk WAF with an upgrade.

Note that one quirk is that there
is a as-of-yet unresolved but for the Linux Intel GPU driver that involves tearing during video playback. But, there is an easy workaround, and that is to use OpenGL for rendering the video. This is what I do, and I have no tearing. But the tearing is quite obvious otherwise (also note, I didn't see any tearing when using mplayer-vaapi).
As for the much publicized 24p issue: it's a non-issue for me. Either my TV somehow corrects for it, or it's simply going unnoticed. Even if I have the problem, but can't see it, I'm happy---ignorance is bliss in this case!
Having said all that... I think you could duplicate my setup (i3-2100 + Asrock H67M-ITX) for a reasonable cost and have a perfect Linux HTPC platform. You could go with a cheaper CPU, like a Celeron or Pentium, but then you'll
probably be forced to use vaapi for HD playback (i.e. hardware-based). I've yet to use such a CPU, so I can't say for sure if they have enough grunt to do software-based HD playback---but they should definitely be able to do hardware-based stuff.