There's a lot to think about here;
Media Centre Edition is not (AFAIK) available as a standalone product. If it is, then it's probably an OEM copy that is potentially being sold in breach of Microsoft's EULA. (See the Forum Ed's blog on that subject for more details)
A standard copy of XP Home Edition will do most (but not all) of what the MCE can do. You'll probably want to add a TV Tuner card and recording software such as Showshifter
What format are you going to build? ATX is the easiest and most economical choice, but less that ideal for a living room environment unless it can be tucked out of sight. It is certainly possible to build an almost silent yet quite potent ATX system for reasonable cost. A Small Form Factor case is a potentially trickier proposition, but would fit well in a living room. The third alternative is one of the specialised Media Centre-style cases that are now available, that allow you to build something that fits in with your existing electronics products.
Perhaps your best bet is to buy off the shelf. With regard to the third type of case that I mentioned, companies such as Hi-Grade produce some very nice MCE systems for around £1000.