Ok, first off, this is probably a bit over kill and you have to find the TV tuner/capture card as I haven't looked in to them for over a year. You will also have to figure out the case
AM3 Athlon II X2/X3
ASUS AM3 EVO 785G HDMI mATX
2-4GB DDR3 1600 GSkill or other top brand (Corsair, Patriot,etc)
2x1TB Samsung F3s or more
LG BD Burner (this: http://www.newegg.com/Product/Product.aspx?Item=N82E168... )
If you want quiet: Get a Hyper 212+ and replace the fans with some Scythe Gentle Typhoons or Slipstreams or get a quiet Noctua.
Well...if you want to save some money, try buying an i3. They make excellent HTPC processors with their integrated graphics. The processor is packed with features that make the excellent HTPC processors. Hopefully I helped!
I think I will hold off on the tuner card for now until I do some more research. I have comcast digital cable with a Cisco RNG 150 box. For my receiver its a Marantz SR7002. My main focus is around a clear picture and crisp sound. Occasionally I will do some internet browsing but this is not my main reason for an HTPC. I want a clean inter grade with my home theater. If i go with the core I3, which mobo would i have to use?
Imo, going for an i3+ a decent H55 board is pretty expensive. Stick with an AMD for this kind of work. You will probably get better performance overall with a good HTPC card like a 4550,etc over the IGP in Clarkdale. I'm nor saying that Clarkdale is bad, but rather an bit overkill in cost when considering total cost for CPU + board.
The best mobo onboard video out there are AMD and HD 4290 is the latest. People even game on those so it's no problem to run 1080p movies.
About the CPU integrated videos I don't know much but maybe it's better to leave the CPU do its business and use the onboard video card like in the AMD solution. Also, as Shadow703793 said, it's overkill. Also the i3 has a TDP of 73W compared to AMD's 45W - that's more heat in your system.
For digital cable you need a tuner with DVB-C. I have an older Hauppauge myself (HVR-1300) and it's very good only it has only DVB-T (digital signal over antenna), I guess the newer models have DVB-C as well.
For the sound (Dolby, DTS or whtever you'll be using) ask on the audio forum or on a dedicated forum like this one: