if I copy my /home (someone said /etc too) over to my laptop, and back it up as well, I’m golden?
/home yes., but ideally only files and dirs starting with a dot (so called “dotfiles” under your home dir. tar cvfa homedots.tar.gz /home/username/.??* should take care of it.
Please note it will include some large stuff that’s probably not needed, like .cache, or some individual caches for other apps that don’t use .cache, like the browsers.
Don’t copy /etc, it’s usually machine-specific.
would different hostnames and usernames make a problem?
Hostname no (if you don’t bring etc). Username technically yes, you may want to rename the home dir. The user id and group id are important too but usually off it’s the first user on the same distro it will receive the same ids (typically 1000 nowadays). If not, you can change that manually and recursively chown 1000:1000 -r /home/username.