If you are going that route, I'd probably say go with an AGP AIW 9000 or 9200. They are typically $30 or less. Those require the easy-to-find/cheap purple domino dongles and will either have DVI or VGA out without needing an adapter for the graphics card part. They all use the same Theater 200 chipset.
For the motherboard, really any AGP slot containing motherboard with SATA connectors should be more than modern enough to not drop frames and will use a Pentium 4 or newer most likely which will meet the hardware requirements of the AIW card. You don't really have to go nuts on the ram either - 1GB is probably fine. I'm not sure if there's any reason to avoid AMD processors, but I usually see these capture PCs using Intel P4 or later processors.
Other thing to note is that basically all AGP containing motherboards won't really have a way to get the data off of the capture PC in a particularly modern/fast way. Fastest would probably be to just disconnect your SATA capture drive and connect it via a separate SATA to USB 3 adapter to your modern computer for deinterlacing etc.
You can build such a computer for probably $200-$250 and that's with one SSD for the OS and one for the captured files to go on. If there are any E-Waste or computer repair shops, they might even have some older tower PCs that fit the bill, or you might even see some on Facebook marketplace or similar. Basically just needs SATA ports and the AGP slot.
There are PCI-E versions of the AIW cards that still have the theater 200 Chip, but they run hotter and I think more of those had the harder to adapt video inputs and display outputs.
There's also the TV Wonder USB 2.0 that you can essentially connect to any XP machine via USB 2.0 and that also uses the Theater 200 chip. The main downside to the USB TV wonder is that it can't do MPEG2 compression if you want to capture that way (takes up way less space, but isn't exactly lossless - good for DVD or decent copies that you don't want to take up much space). But if you were planning to do lossless
Huffyuv capture anyway, the TV wonder should perform the same in theory to the AGP cards, but I don't know that I've seen an actual direct comparison capturing from the same source to show that.
I'm not saying the AIW is the best of the best, but it's probably going to be better than a random capture card you find used at Goodwill or on
Amazon, though there are some pretty good reviews on the GV-USB2 and Startech cards that do work with modern Windows computers.
If anyone has some direct links showing the GV-USB2 vs a Theater200 AIW card, I'd be interested in checking it out.