Yes, the differential method is an accepted way to display waveforms without a GND reference.
This is my first scope ever and I have no experience with using one whatsoever so please bare with me.
Don't plan to run before you can walk.
Get some experience on low power, low energy circuits first.
After many years using DSO's, I always look for another way rather than expose myself or my gear to any risk.
Mistakes are just too easy to make, more so for the inexperienced.
Since the OP is a beginner in Electronics, I'd suggest staying away from the Mains and working with 15V or less.
PS why scope the mains anyway? What are you looking for?
Not exactly a beginner. Just new to oscilloscopes
I am looking to see how clean of a sine wave I am getting and to check for high voltage spikes in the signal.
I would also like to compare the mains output to the UPS output.
There WILL be spikes and all sorts of rubbish on mains, accept it and get used to it.
Get the UPS manual and read the class of output it provides.
Stepped or pure?
Do you have a problem with equipment the UPS powers?