'... inherited the setups ...' ... always 'fun' :| Always an 'adventure'. As far as always doing a 'clean install' that has some advantages, but depending upon how involved those are, one might eventually grow to a point of wanting to do things more easily/efficiently. That comes with time/experience.
First recommendation ... setup a tinker box (Debian cause that's what your production machine is) ... doesn't have to be powerful. For a while, think I'd use the tinker box to try things out rather than back yourself into a corner by working with a production machine and making a 'boo-boo'. Could setup a Virtualbox Debian on your laptop/workstation.
http://www.brianlinkletter.com/installing-debian-linux-in-a-virtualbox-virtual-machine/
Learning Linux ... am probably the wrong person to ask what would be the easiest path due to my 'history' but will suggest, if one has Debian then go to the source:
https://www.debian.org/
Off that page one will find a wiki: https://wiki.debian.org/
LIke Moodle Community forums:
"This wiki is a support and documentation resource for the Debian project. It is editable by everyone and we need your contributions to make it better."
NOTE: some community forums are more friendly than others but be bold ... polite but BOLD!
Areas specific to Moodle: PHP, MySQL (if using MySQL), and Apache. Each of those have their own home pages and info.
Then there are notable blogs ... haven't really found one yet, but ... it might be a good starting point for your journey:
http://www.2daygeek.com/best-websites-blogs-to-learn-linux/#
At this point, invite others to share their experiences even if these forums are supposed to be about Moodle.
One last suggestion ... put your operating system, versions information in your profile here in Moodle OR when you post a question, include some technical info ... like Debian version, PHP/MySQL/Apache versions, etc. so folks that want to help have some info to go upon. Reporting the 'thingy broke' will beget nothing but more questions rather than the help you seek. ;)
Considering the recent 'changes in attitude' by Microsoft towards Linux in general recently (Microsoft has joined Linux Foundation and other similar 'events' - developing their own Linux to help with Linux guest OS's in Azure, developing an MSSQL for Linux, and am sure others will follow) you are beginning your journey just in time. ;)
'spirit of sharing', Ken