HDMI capture card for capturing TV in an HTPC?

So I have a spare PC, and could use a way to capture broadcast TV sometimes.

so recently our cable company switched to digital only, and makes us rent a box which is fun, it's not actually possibly to buy it. but it's basically a tiny cable box.

and the box does have coax out, but HDMI is going to be better naturally.

So what exactly do I need to build an HDMI capture box? I would imagine an HDMI capture card, preferably PCI-e, but why are they all so expensive? and they mostly seem to have poor reviews. Is a USB one just fine?

Does the capture card just come with software that will passthrough the signal for the PC to TV?