Good grief it's taken me a while to get back to you - so sorry about that! =/
The answer to your question could fill pages upon pages, and would vary greatly between sound designer. One of the most fun/challenging/scary/liberating things about sound design is that there really is no "right" way to go about things. It could start with being in a subway station and hearing a really weird, defective elevator door motor. Maybe that motor sounded like a grumpy, tired robot grumbling about something. So you grab your trusty portable recorder, (Zoom H4n, etc...) record that weird elevator door, and stash it in your personal archives, knowing it'll come in handy some day. Being aware of your surroundings, and listening to all the crazy sounds that most people ignore is a great way to develop an ear for the unique.
As it pertains to designing sounds for new Champs, or anything else in game for that matter, generally the approach is, "How do I sell the flavor, character and emotion of this Champ with a set of sounds that is fiercely unique to them and also allows for the highest level of game play clarity?" No two Champs are the same, nor should their sonic palettes be the same. You should know which Champ you're hearing at any given time, even if you can't see them.
So, how do you do that? We figure it out as we go, every single time; like I said, there is no right answer. It takes experimenting, knowledge of the Champ's back-story, knowing how they'll behave in game, and how players are likely to build them.
Often times too, the area or faction from which a Champ hails will have a direct effect on how that Champ should sound. For example, most Champs from the Shadow Isles all share a common tonality, while maintaining their own unique sound.
Let's keep this conversation going - I'm sure that didn't answer all of your question(s), and I'd be happy to go back and forth on this. =)