Read this whole chapter until you understand all the concepts.
https://www.allaboutcircuits.com/textbook/direct-current/chpt-3/importance-electrical-safety/Also how effective is an RCD in case my scope ground wire accidentally touches a live part of the circuit I am testing?
Draw the circuit out (best way to learn). You want all your test equipment on RCDs even an isolation transformer if you have one.
The RCD will definitely not save you in all situations but can help with equipment failure or if you accidentally trip it you can hopefully limit the damage to you and your equipment.
One option would be to buy a differential probe but that is quite expensive. The other could be an isolation transformer to isolate the equipment I am testing. Could you comment on pros and cons of both options?
Would this be an option?
Battery power oscilloscope with appropriate rating and isolated insulated inputs (handy).
High voltage active differential oscilloscope probe (bandwidth limited to probe, isolates and lowers voltage to the oscilloscope input).
Isolation transformer (doesn't isolate high voltage from the oscilloscope probe/input, isolates DUT from mains*)
High voltage probe (allows you to measure high voltages i.e. 40kV with the appropriate probe, can be very limited bandwidth)
Note: They all require you know what you are doing but with an isolation transformer you can easily undo any perceived safety by attaching additional equipment (one of many ways in fact). You should not rely on any device to keep you safe it's more about knowledge and a systematic approach to safety.
The link you posted is an auto transformer, it has no isolation. Isolation transformers have various different wiring schemes. I've not seen a suitable purpose built isolation transformer for sale here in Australia. We refer to ours as a bench safety isolation transformer or a technicians isolation transformer, ours are wired with the intended purpose of providing a fully floating mains source. A medical grade (or quality) isolation transformer may have additional safety features. But never assume anything is quality or is ever wired correctly because they often aren't.
I'll add a tip to those provided, always know the circuit you are probing and where the different voltages are, you can easily exceed your equipments input and less likely to learn what a Cockcroft–Walton ladder is the hard way.