The mildly annoying part is most DSLRs don't have an AC adapter input to allow them to be constantly on, but you can buy a "fake" Canon battery that sits in the battery compartment and wires in AC adapter input.
Yeah, I left out that detail. One should also make sure that the camera has a clean HDMI output. I can't use my old EOS 500D for this since the HDMI output is grody with focus aids and stuff.
If you're on Linux there's a way to make this work with gphoto2, but it involves a little bit of fiddling and is less plug and play.
The thing with shooting WFO, you'll have tissue paper thin focal plane. Moving forward or leaning back could throw you out of focus.
Honeypot!
b) if you presume "mirrorless camera" as a baseline, a prime 1.x at roughly 50mm (equivalent) is almost always one of the budget lens options.
If you are not on a budget, you can use a mirrorless camera with a big aperture (say f1.6), wide angle lens as a "webcam" by connecting the HDMI out of the camera to the computer using an Elgato Camlink. That will also get you a nicely blurred background.
I do this, and a lot of people do a double take whenever I enter a zoom call. Best commment so far was "What is happening? Are you in a movie?".