Camera model Do not have camera, looking to get a webcam for as cheap as possible, but not sure what is supported by raspberry pi 3 and what is not.
Logs (/var/log/webcamd.log, syslog, dmesg, ... no logs, no support)
Additional information about your setup (OctoPrint version, OctoPi version, ...)
Just installed octoprint in the last 2 weeks, so I am new to all of this.
logitech c270 are cheap (when bought used) an do the job.
don't go dead cheap because the mostly have no hardware mjpeg encoder.
Then you need a bigger hw to render webcamstream from still pictures to include it in octoprint.
Nur so nebenbei wenn du das nativ lesen kannst gibts die C270 grade reduziert auf 17€ neu bei Reichelt 
Well if you want it as cheap as possible I would go with a raspberry cam clone.
Depending on where you buy it you'll get it for 5€.
i had some raspicam clones which were horrible.
they had only a really dark picture.
I have thrown them away.
My only genuine one got gina for her dev rig