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The hardware considerations when designing a Home Theater PC are a bit different from those when building a gaming system or a workstation. Because Windows MCE requires each TV tuner to have an encoder chip for handling recording, and because modern video cards do a great job with video decoding, the CPU in an HTPC is, surprisingly, one of the least-important parts. Unless your computer will also be used for other tasks, a low-end single-core processor will do fine. If you plan to use email and internet as well, a low-end dual-core processor might be a better choice (as it will make multi-tasking much smoother), and for combo HTPC/gaming rigs the sky is the limit. Keep in mind as well that lower-speed CPUs draw less power and generate less heat - meaning that less cooling is necessary and therefore the system is likely to be quieter overall.
Memory is also not a huge deal, as generally the only program running will be Media Center. 1GB is probably a good starting point, and again get more if you plan to use the computer for other tasks as well.
The more important hardware choices for this type of system are going to be the hard drive(s), video card, TV tuner(s), and (perhaps surprisingly) case. The hard drive is important because it is going to be holding any TV recordings you make, as well as any music and video files you want to store. Normal TV signals (not HDTV) take up about 3-3.5GB per hour, on High quality. I personally recommend having 30+ hours of recording space (a minimum of 100GB) just for TV, and then another 50+ GB of storage space for music (either ripped from CD or downloaded via an online music service) and video files. Based on those numbers, plus having room for Windows itself and any other applications you might want to install, a 250GB hard drive is an excellent choice. You might also consider going with a smaller system hard drive and a separate drive for media storage, or even potentially a RAID 1 array (so that if a drive fails you don't have to re-record/rip/download your files again - for more info on RAID, see this article).
A video card is also a significant part of a Media Center system, because it is responsible for connecting your computer to your monitor or TV and giving you a good, high-quality video feed. The reason that the choice here is important is that you don't want to go overboard, but you want to make sure that the video card has the right connectors to support your TV/monitor. Almost all video cards these days have one (or sometimes two) DVI connections, which can usually be adapted to support older VGA monitors as well. Many cards also support S-Video, and mid-to-higher-end cards come with adapters to provide HDTV signals via Component Video cables. Some onboard video solutions also offer these features, and again as long as you are just playing back media (and maybe surfing the web) you don't need much power from your video card. Unless you are gaming, you will want to avoid the high-end cards because they tend to put out a lot of heat and require fans that generate a lot of excess noise. If at all possible, either an onboard video solution or a passively cooled video card (one without a fan) is going to be the best way to go.