Got An AMD Athlon XP 2200 here, with 512MB of RAM and an FX5200 AGP card. It also has a PCI video card in it and runs two monitors smoothly.
I don't know how demanding the TV tuner and recording programs will be. I'd guess you might be able to increase RAM to 1GB and get a better video card and get along fine with this. But, again, this is somewhat of a guess. Those two upgrades would leave you well under $500.
Now, if you want to go further and replace the motherboard and processor, I'll leave that discussion to others here in the forum. However, this should all fit into your $500 budget.
You know, you could just go ahead and install the TV tuner in your current system and see how it goes before deciding on any upgrades.