Lemme see if I can shed some light on the original question, but keep in mind this won't be as detailed as I'd like to be.
A good preamp should amplify the mic sound without adding a lot of noise to the signal. That's its main job - make the mic signal louder. Some preamps (like the Great River, for example) are clean, transparent, quiet, and give great results when you plug any mic into it. But that's not the end of the story.
Distortion is not always a bad thing. Some of the early preamps had a lot of distortion (up to 5% or so) and limited response but they still sounded great. Why? When some electronics reach their upper limits, how they distort can be very important. When tape reaches its limit, it "saturates" and can sound very full and rich on some types of music, even with 3 to 5% distortion.
In tube equipment, "even order" distortion can also make the sound fuller. Output transformers can produce wonderful saturation distortion, but these colors are by-products of the original intent.
Some preamps are designed to stay clean and clear, regardless of what is being put into them, while others will produce a pleasing (or unpleasing) coloration. But using that coloration on everything is not always desirable. It's a matter of taste.
For my own recordings, I prefer to go with clean whenever possible, and add any coloration later. Most of the low cost preamps currently available add some form of distortion and coloration. Don't ask me which ones because I haven't listen to that many of the new preamps.
Anyway, I hope this helps.