What PC do I need for 4K video capture?

It depends on the interface. A USB capture device needs a USB port fast enough for the video it sends, and a PCIe capture card needs a free slot of the right size in a desktop PC. The most common 4K capture problem we see is not the capture device at all. It is a USB port that cannot carry the data.

USB capture, single device: uncompressed 4K at 60 fps is more data than a standard USB 3.0 port (5 Gbps) can carry. 3840×2160 at 60 fps in the 12-bit NV12 format is about 6 Gbps before any overhead. That is why the 4K60 models, the USB Capture HDMI 4K Pro and USB Capture SDI 4K Pro, have a USB 3.2 Gen 2x2 interface rated up to 20 Gbps. For 4K60, connect them to a port of that speed with a cable rated for it. If your PC only has USB 3.0 / 3.1 Gen 1 ports, capture 4K at 30 fps instead. The USB Capture HDMI 4K Plus does that over standard USB 3.0, and still passes 4K60 to a monitor on its loop-through.

USB capture, multiple devices: the sums add up quickly. Uncompressed 4K at 30 fps is about 3 Gbps in NV12, and 1080p at 60 fps is about 1.5 Gbps in NV12 or 2 Gbps in YUY2. Many PCs share one USB controller across several ports on the case. Plug two 4K capture devices into ports that share a 5 Gbps controller and together they ask for more than it can carry, even though each port is rated for the speed. For two or more capture devices, give each one its own USB controller, not just its own port. Check your motherboard's controller layout, or add a PCIe USB expansion card with a separate controller per port.

PCIe capture: avoids the USB limit. The card sits in a PCIe slot on the motherboard, so several 4K channels are easier to run than several USB devices on shared controllers. Magewell's single-channel 4K Pro Capture cards, such as the Pro Capture HDMI 4K Plus, use a PCIe Gen2 x4 interface, and the dual-channel 4K cards use PCIe Gen2 x8, so check that you have a free slot of that size. The trade-off is that you need a desktop PC with a free PCIe slot, not a laptop. For compact PCs with an M.2 slot, the Eco Capture M.2 cards are the alternative.

Storage and CPU: this part is general video-production advice, not specific to any capture card. If you record 4K, as opposed to passing it to streaming software, the drive must keep up with the data rate you write. Uncompressed 4K60 runs to several hundred megabytes per second, which is beyond a hard disk or a SATA SSD, so use an NVMe SSD for that. Recording with a compressed codec needs far less. The CPU matters mainly when your software encodes live, for example OBS with software x264. Capture itself places little load on it, because Magewell cards do their scaling, de-interlacing and colour conversion in their own hardware.