If you're looking to find what distortion signature you like here is an exercise I went through myself. In a DAW, I used Reaper, instantiate a tone generator plugin, saturator and an EQ with an analyzer. All on the same channel. I used Fab Filter Saturn 2 and Pro Q. All of these have a trial period long enough to do these tests. Start experimenting with tones to see what the harmonics look like. Make some presets with varying degrees of Second, Third etc...harmonics added. Then play your music through your presets. You'll probably develop a preference. Then select equipment that tests similar to your preference.
Generally speaking, if the signature is plainly audible on familiar music it's most likely a poor design or broken. Differences should be very subtle in well designed/built gear.