Check the Wiki for "newbie packs" for ideas.
Pretty much any dual core processor is fine, above 2 GHz. I chose an AMD 4850BE which is a dual core 2.5 GHz, low power 45W. Around $100.
2GB of memory is heaps. Around $50.
Choose a motherboard that has an inbuilt Nvidia graphics chip. I tried one with a decent built in ATI one, and LinuxMCE did not play nicely with it at all (some others have reported more success, but I could never get the new UI to work properly with it).
Motherboard with both Analogue and digital (optical) output, Realtek ALC chips have fairly decent support.
Motherboard should be around $100-$150.
2 Ethernet ports are pretty much required. One probably on motherboard, add another if required ($30 or less).
Digital tuner for DVB is your hardest choice, because many manufacturers bring out a tuner that works with Linux, then change the chipset to one which doesn't work well. And keep calling it the same model. I'd avoid the dual tuner models, as both of mine have been problematic. Avoid the Dvico Fusion 4 HDTV, it is intermittent with LMCE 7.10 on some motherboards (mine!). Latest list is at http://www.linuxtv.org/wiki/index.php/DVB-T_Devices
. My Pinnacle dual tuner USB stick (2001e) is a pain 'cos the 2nd tuner never worked well, and it has a stupid micro coax connector.
My problems may disappear once I manage to get the Linux kernel updated.
Get an HDTV tuner, you can remove the HD channels from the lineup you see so you don't waste space recording HD while you don't have an HDTV, or you can just use Mythtv to force a recording on SD channels. Remember that some programs are only appearing on HD channels now!
Due to channels overrunning their schedules, buy AT LEAST 2 tuners. I found 3 was the right number. You should be able to pick them up for $50 each for USB tuners.
You may need a masthead amplifier and a splitter for your 4 TV antenna leads (3 to computer, one to TV). It is a good idea to have a 75 Ohm terminator on any additional unused antenna points- check http://www.laceys.tv
catalogue for some tips and ideas (near the back).