Character animation and cloth are two things that build up on each other. No cloth will work properly without a good rig and character/rig-building skills.
I see character animation as a top-level skill, as it is based on many standard and advanced animation techniques. Nothing that is just done or based on a do this, do that tutorial. In other words, take your time, and let it grow. I assume you toss that advice, but I had to say it 😉
The primary skill is undoubtedly in directing and being an actor simultaneously. My definition of a director is that they direct the audience, only secondarily the actor or the character. I suggest taking acting classes, or at least some courses; I loved the acting classes at "Masterclass.com" to get better at it.
If you use a Motion Tracking Volume or a "Performance Capture suit", as we call it, some skills need to be acquired.
From my point of view, having natural-looking cloth on a character is a step above the character animation or acting skill set.
To answer your question, first of all, why are there wrinkles in the cloth, and how would they behave and change with the character?
Anything on a character supports expressing something to create information for the audience. This leads me to my question. To get there is not a "do this – do that" path.
If you like to use displacement for that, I would think (while answering a super general question here, without even a sketch received!) that you need to be able to connect it to the character's expression. Every wrinkle will flatten if that area is stretched. That can be done in many ways. It would fill a lot of space to explain all options; let's focus first on the next steps.
Here are two courses for the very first basics of character animation:
The series is
Intro to Rigging in C4D: Part 1 - 6 Fundamentals of Rigging
ZBrush Character Creation, Cinema 4D, Redshift 3D 1-6
As a side note:
Since you already have a very defined idea, so far, I can tell; The easiest way to get into Cloth Simulation is to use tools that are 100% specialized in this. Please explore this, as it will give you many ideas and perhaps some answers. https://marvelousdesigner.com/product/overview
Images do not tell me a lot, but I can see it has two arms. I have no idea about this object, and Turbosquid has a few skeletons on its site. In other words, I don't know how it is created.
There are two main options; why do you see two arms after rotating? The first one, the Command/Control key, was down (and has created a copy, or the setup has two skeletons and switches between the two to provide IK/FK options while avoiding a Joint based setup. Both are guesses, and nothing that I like to do here.
So, go to the Object Manager> Object> Project Information, and check how many objects are in the scene. Close it. Rotate the other arm. Get the Project information again and check if there is now one more object.
This will answer if you have a new copy or the setup is done this way. (While both are visible based on a setup, that would lead to problems later on. Again, these are just guesses. I would need to see it, but you can post it in public. You could send it to [email protected], and I have a look at it. Please note, I do not move the discussion to email; that needs to stay here, so many people hopefully benefit from it.
Yes, there are certainly a lot of tiny little tricks that need to be shared. Having done the timestamps for the past 11 episodes for the Hands On Character show, I believe we can quickly fill a third season with tips and tricks while going deeper into the tech. But I fear those solutions are more interesting when needed during a project, not presented in a more extended series.
With that being said, I hope to fill those gaps that are naturally left and learn from everyone's questions I got over the past nearly two decades.