Spectrum analyzer vs. FFT capability

If I want to see the waveform of my fundamental frequency and the distortion, do I need a spectrum analyzer? Getting an oscilloscope that can do FFTs will show me the magnitude and harmonic characteristics of distortion, but I assume it can't show me the waveform like above?

You can get scopes with FFT display too.
I designed my own scope + spectrum analyser for audio.
It works via USB to pc display.
 
Here is a shot from my scope/spectrum analyser.
fft.jpg
 
I have not had really good value from the Siglent FFT. It works and you can get a rough idea of the spectrum but nowhere near as useful as a PC soundcard. The Picoscope FFT is much more useful. Still the PC soundcard has worked better. You have numerous choices for software with a PC.
 
If I want to see the waveform of my fundamental frequency and the distortion, do I need a spectrum analyzer? Getting an oscilloscope that can do FFTs will show me the magnitude and harmonic characteristics of distortion, but I assume it can't show me the waveform like above?

I have a piece of test equipment that has Spectrum Analyzer, Receiver and FFT capability in one unit on my day job. This is in the 10 kHz to 18 GHz range but the principle is the same.

Each has is optimum application.

The FFT is very fast. It can capture and process the information in seconds.

The tuner is second but it does not capture all of the information in the complete range selected. It looks only at discrete frequencies.

The Spectrum Analyzer is typically the slowest but affords maximum information, sidebands, spurs, harmonics etc.

A scope with FFT function should be more than adequate for your analysis.