Can I install a PC/Server at home and bring it to a public school?
Would changing the IP address be the only thing I would need to do?
I am a teacher at the school.
"Would changing the IP address be the only thing I would need to do?"
Nope, more than just that! Much to consider and you still might not be able to ....
First, your provider for your home connection to internet. Normally allow traffic outbound **** but not inbound ***.
In your boundary router you would have to allow at least port 80 and 443 traffic to your PC.
Next is DNS - site accessible by fully qualified domain name that goes into config.php ... that has to be entered into DNS systems somewhere! And the IP address would have to be the IP address your home router pulls from provider - provider could change that IP address at any time and without your knowledge nor permissions to change.
Next is your PC ... Windows ... UGH! The most attacked OS on the planet and the software you install to run a moodle ... XAMPP etc. not designed nor recommended to use for a production moodle.
Senario ... you are at school and there is something wrong with the moodle that could be fixed if you had access to the files ... now you need to open up windows file sharing ports 13x to get to it that way .... or FTP port ... which means your Windows server will also have to run an FTP service.
For all reasons above, not a good idea to try to host from home.
You are better off hosting with a provider and using Linux ... not Windows. Cheapo shared hosting ... which means you might struggle with resources of the server - depending upon number of students/course/how often hit (blended - teachers and students using in class live or sync - same as blended or async - students use as extra after F-2-F class time).
My 2 cents ... but what I've shared is from first hand experience.
'SoS', Ken