RJ45 did work, but Pi Zero froze when connecting something to USB.
Then I did read "We've tested heaps of these adapters and this one is by far the best!" on pimoroni.com (where I bought two of my 4 Pi Zeros) for their "Three Port USB Hub with Ethernet - microB connector":
https://shop.pimoroni.com/products/thre ... -connector
Although that one costed £10 plus £4 shipping I did buy it, it arrived 5 days after shipping (over the weekend) and just works. I did connect 3 cheap 2$ USB cameras (a fake 5M camera, but really good 0.3M, see report) to it and ethernet:

After identifying the Pi Zero IP address with "nmap -sn 192.168.178.1/24" I did "ssh -X pi@192.168.178.124" with X11 forwarding. Started "eog X.jpg &" with X in {4,5,6} to view the image taken by the USB camera "/dev/videoY" with Y in {0,1,2}. The images get shown on Laptop by X11 forwarding and get updated when new picture gets taken by "fswebcam -d /dev/videoY -r 320x240 X.jpg". The photos of the cameras do show the other camera(s) [right click for bigger screenshot]:

Summary:
£14 is not cheap, but a good price for quick delivery and working well.
Hermann.