In the MCE FAQ there is a link to supported MCE components.
Basically, I would recommend a 3 to 3.5ghz CPU, 1gb RAM, an nvidia 6150/6200/6600 with purevideo codec, lots of hard drive space, quiet/silent cooling and a funky case. Oh, and twin tuners and a cool plasma/lcd display.
I would suggest getting the best components you can afford. I built mine a whille ago and the components I used are pretty cheap now. I have:
P4 2.8 £100
Geforce 5200FX video £30
Asus motherboard with onboard 5.1 sound £50
2 blackgold digital tv tuners £106
1024MB RAM £60
160BG 7200rpm HD £60
Pioneer DVD writer £30
CD writer £15
Card Reader £10
Digitalis Vision II case £120
MCE remote £30
Silent cpu cooler and system fans £30
Total cost £581
This spec might not sound very up to date but my system works flawlessly (never crashes), the tv picture is superb, it boots up quickly and has plenty of storage space. Downside is it is pretty big. The case is very nice brushed aluminium but is big enough to house an ATX moutherboard and full size PCI cards.
I just built a budget system for my dad to replace his yamaha HD cd player. I used the following components:
mediatv.pc case with infrared reciever and mce remote £112
asus Matx motherboard with onboard sound £50
512MB RAM £30
blackgold digital tv tuner £60
Intel celeron 2.8 CPU £55
geforce 5200fx video £30
80GB 7200 hard drive £40
pioneer dvd writer £30
The total cost of all of this is £407. I would say the main difference in terms of performace compared to my own system is the ability to record two channels at the same time. His system is also noisier than mine but this is not so important as his living room is about twice the size of mine. The only other difference in performance is when watching tv and then pressing the power button to shut down the computer his takes a wee while (about 10 secs) before shutting down (I have configured both systems to shut down rather than go into standby). I put this down to the ram but plan on buying him another 512 stick for his birthday next week.
Anyway, I have forgotten why I stsrted this....oh yeah, minimum spec. If is is only used as a htpc, ie nothing else but media center then the above spec can handle it fine (but go for 1024 ram).
Hope this helps.
before asking the question you should decide what your HTPC needs to do, a Sky setup ise very different from Freeview dula tuner, and some people just want playback. That dictates very quickly how much you want to spend eg dual tuiners and a large hard disk is say £150 more.
I would suggest that you can spend £400-600 for a base machine, that really works or get a silly spec for £1300+, really depends what you need it to do and your abilities to buy v build.
You should also have a think about intended output resolution as that affects the graphics card and CPU you might need.