Hey OP!
I’ve done this before and I have some thoughts. DIYaudio is a better place for this type of hackery. You should have a 10:1 or 100:1 probe for your scope.
The thing I learned though is that an oscilloscope by itself is not actually very useful except in seeing really gross issues. For instance, I had an LED lamp which caused audible buzzing and you could see the "bite" the power supply took out of every positive going AC cycle. The bad news is that unless things are gross you don’t really get any sense of how good or bad the AC waveform is. For this you need to know things like harmonic distortion and/or a spectrum analyzer. First will give you a basic readout of how close to ideal the wave shape is, second will tell you more or less where in the frequency spectrum your problems are.
You might want to consider a PC based software solution, which uses the audio inputs, and maybe a custom, isolated interface to prevent the risk of injecting raw AC into your PC’s audio input. There are some good online resources for how to make one of these. The limiting factor here is maximum frequency response will be limited to about 20 kHz. You won't see any RFI noise this way.