I use the internal Elgato HD60 Pro for my playfield cams. I also use the external Elgato HD60 S for my score cams. I’m sure the CamLink works just as well. Others use AverMedia. They should all work without much issue. You might consider an internal capture card so that you can spare some USB bandwidth for your webcams.
Lots of advice relating to the C920 earlier in this thread: mainly to turn off Auto-Focus and Low Light Compensation (especially if you are getting extra lighting). You may or may not want to set them to 60FPS – they unfortunately have lower quality at 60FPS, but for something like a tilt bob cam it won’t be noticeable and the extra FPS would be cool.
I use the CX-405, they work nicely but I’m also on the lookout for other options. Note that the camera uses Micro HDMI, so you may want to scope out a longer Micro-HDMI cord or an HDMI->Micro adapter to have on hand. Also, you’ll want to plug the camera into the wall for long sessions. It comes with a power adapter, but I use a USB power pack veclro’d to the camera stand.
I don’t have any experience with the DMD Extenders, but TNA outputs both video and audio over its HDMI signal, and you’ll need an extra camera there for the score displays.
If you can get the audio from the croc clips to a 3.5mm jack, you can just plug it into the Line-In on your PC and add this as a Microphone Device or Audio Input Source to your OBS scene. You may or may not have some issue mixing the USB and analog sources (USB will be delayed slightly, so there might be echo). I usually settle for this when I stream on location. But if you want to get a littler fancier, you could get a mixer and an XLR mic instead of the Snowball. The Behringer Xenyx USB mixers that @chuckwurt mentioned are all nice and relatively cheap.
Always nice to see new pinball streamers, good luck!