Choice of CPU for the PC is between a P4 650 HT 3.4MHz, 2MB cache, 800MHz and an AMD Athlon 64 X2 3800+ dual core processor. I had a quick look on the internet and it looks as though the AMD has the upper hand.
Get the best spec you can if you are not paying, although you might have to work harder to justify the investment -
Both would suit your requirements, I would go for the AMD also - may cope with future technologies better.
12ms would OK for watching TV also.