Not the parent, but I use a Logitech 920s webcam. I could use one of my high-end cameras--I even have an older model Fujifilm I don't use any longer--with an HDMI to USB converter but I decided it wasn't worth the trouble and it's harder to make work in physical space anyway.

I use a Blue Snowball mic but any decent USB mic will work. I have a dedicated office and I haven't found using a headset makes it better though YMMV. I'd just as soon not wear a headset unless necessary.

Computer is just a 27" iMac with a 2nd monitor. (Though I actually usually work with video on my main screen and do any work with shared docs etc. on a MacBook.)

Also have an Elgato keylight to get the lighting a bit more even.

ADDED: Probably at least as important is that you're not backlit by a window and you have the camera at maybe a bit above eye level. I've also done a bit of "set decorating" of my background.

Logitech BCC950: https://www.logitech.com/en-roeu/product/conferencecam-bcc95...

If I had the extra space and time to set it all up I would probably use a regular SLR camera on a tripod, and lavalier mic. But the Logitech is a lot more convenient - connects over a single USB through the docking station and just works with zero set up.

The screen is just a regular LG 4K 55" TV mounted on the wall which connects to the laptop docking station, allowing video conferences, slides, etc. to be "thrown" over there when it's convenient.