Blackmagic all the way, we used them extensively (still do) at the beeb. Their linux driver support is excellent too, the only maintenance I ever needed to do as a sysadmin supporting a fleet of these was occasionally update their firmwares.
A note on Blackmagic hardware in general (including the ATEM switches)- they tend to only work with signals that are fully compliant with broadcast standards. For example, I have some Cisco HD PTZ cameras with a "raw" HDMI output that sends 1080p30 or 1080p60, but there's some wacky difference in the colorspace they output such that my Atomos recorder and Blackmagic capture devices only lock sync when the video level (brightness) of the scene overall is low, such as when you put your hand over the camera. The same cameras work fine with the $25 generic USB capture devices, as well as with the Avermedia BU110 which should be a "true" uncompressed USB3 HDMI capture device (that recently was marked down to $60).
I know Blackmagic is a popular brand for actual cine camera equipment, how do they compare to the more common Elgato 4K60 PCIe? Obviously thunderbolt is nice as an interface rather than the add-in card, but is there anything else it offers above and beyond that?
Inogeni devices can be had secondhand pretty cheap. These are FPGA based, and supported by UVC driver (works on most platforms). Firmware update is via a windows app.
Definitely workable but if you want better camera in VC then you may be best going for one that supports h264 or something more modern than MJPEG over USB2. If you've already got a camera then fair enough, get a cheap dongle (or spend a few quid more and get a blackmagic decklink for 99 buck/quid/whatever - PCIe though, but could use a breakout ymmv)
Sure, it was more about cost. If you already have a camera or don't mind spending extra to get one then it'll definitely give you better quality. Having said that a high end webcam can still produce good results so there's a tradeoff somewhere. If you're putting decent source material through a really cheap adapter then I think you'd better getting a decent webcam, personally but it you already have the camera then sure.