It all depends on what you want to receive with it, if you want to do HD
I would recommend a Athlon running at 2ghz actual speed or a P4 2.4ghz
if you are only going for 4:2:0 SD I know that a 1ghz P3 works just fine.
I use 512mb ram in all my computers so I can't comment on how well the
cards work with less ram. If you run a Netstream 2000 decoder card you could do 4:2:0 SD with a very slow computer, I paid $44 for mine about a
year ago but I don't Know how easy they are to find anymore. I got my Twinhan 102g for $59.95 so you could probably get a DVB card and a Netstream for just over a $100 and run it in any computer you can find.
If you want to record and keep allot of stuff for later viewing make sure you get a big Hard Drive.
If the machine will play DVDs it'll work fine with a software-based DVB card.
1.4GHz CPU, 256MB+ RAM along with most models of AGP/PCIexpress graphics card will work nicely.