There is no build of ROS Melodic for Rasbian! There is no Ubuntu 18.04 (Bionic) Desktop build for Raspberry Pi 3! Now what? Here’s my answer:
Flash an SD card with the Xubuntu image linked here (use balenaEtcher):
http://www.michaelvenz.com/2018/09/29/ros-melodic-on-raspberry-pi-3/
The Xubuntu image will require keyboard, mouse and monitor for the initial boot, but otherwise seems to work smoothly. Don’t forget to resize the drive and all that jazz. The cloud-guest-utils is just a collection of utilities for resizing the drive (among other things).
sudo apt update sudo apt upgrade sudo apt install cloud-guest-utils sudo growpart /dev/mmcblk0 2 sudo resize2fs /dev/mmcblk0p2
Once this is complete, you can install as per the Ubuntu Install of ROS Melodic instructions: http://wiki.ros.org/melodic/Installation/Ubuntu