I made the switch from Time Warner Cable's boxes to a SiliconDust HDHomeRun Prime. It was a little bumpy getting started, but once it is up and running - I am saving $60 per month of box fees.
The first thing you need to do - contact your cable company and make sure that a "TiVo box with cable card" will work on their digital TV. If you mention cable card tuner - they won't understand....You might need a switched digital video adapter if they are using the technology (they have to provide this for free).
Second - decide how many stations you want to watch/record at the same time. Here are a few options:
1) Ceton PCI card - Pros - 4 tuners, internal card. Great for recording/watching up to 4 channels at the same time on one PC and/or Media Extenders (recommend XBox 360 or Ceton Echo). Cons: If you share with other computers (not extenders) you have to dedicate the tuner to that PC. It also kicks up the heat inside the box.
2) Ceton USB tuner - same pros as the first choice - but drops one con - the heat inside the box.
3) SiliconDust HDHomerun Prime - Pros - 3 tuners, network connectivity - you can watch/record 3 channels at the same time on any PC and/or media extender. Cons: Network bandwidth is reduced by using this device. If you have 1GB ethernet - not a problem - 100MB could be an issue with 3 streams active.
4) Happauge USB tuner - Pros: 2 tuner device (basically 1/2 the Ceton USB tuner - but half the price).
With multiple streams you need to look at designing the system with 1 processor core and 1GB RAM per stream. So if you are using the Ceton devices, and watch/record up to 4 channels - I would recommend a quad core processor with a minimum of 4GB RAM. I am currently running a dual-core pentium with 4GB RAM and 3 channels are not a problem, but does put a load on the CPU.
Storage - recommend an OS Drive (small HDD or SSD), and a large storage drive (recommend WD Black drives 1TB-3TB). You want a performance drive for the storage drive, because every time you tune a station, you are essentially "recording", and the WD Black drives give you the performance to watch/record up to 4 HD channels without issues.
The Case/Power supply will depend upon how you want to place things. I have my HTPC connected to the big screen. It is fairly quiet, but the case isn't very pleasing to the eye. You can get a long HDMI cable to connect it.
I run a GeForce 210 Silent for my primary HTPC, it is both quiet (no fan) and streams video great. I have also used the HD4000 graphics from my PC without issue. HD video isn't that demanding and the Intel/AMD built in video works great.
If I were building from scratch - this is what I would recommend:
http://pcpartpicker.com/p/SXJS
You can cut a few corners on the build - but this would be a "top of the line HTPC".