I've been trying to get a cloth to fall on a MakeHuman character, and it was hard to do it without cloth crumpling around, or cloth passing through the character in multiple parts. The cloth itself is just a subdivided plane, and I was able to get this working right away by dropping the cloth on primitives.
I tried subdividing the cloth and character, increasing simulation and collision quality, decreasing distance for object collision, activating self-collisions, deleting the MakeHuman helper geometry, plus many other things, but nothing was good enough. After multiple tutorials, one suggested increasing the model 5 times, but I found 10 works better. It seems the Blender's cloth physics are not optimized to handle high poly models of around a meter in size, and you can tell it's taking into account more vertex than it should at small scales since it takes much longer to bake physics. When you increase the size, the effects of multiple variables is effectively smaller (for example, if you scale up 10 times, it's like gravity goes down to a 1/10th, but it's certainly not just gravity), and at times I found a x100 scale gave the desired effect but sometimes it was too much; but at least you only have to change one thing, the scale, in order to get decent results instead of fiddling with dozens of variables hoping you are getting the right combination without any feedback (when you get the right combination it works, but you can't just change a single variable and check if the result is closer to what it should be incrementally, because what matters is the combination of settings, not any individual one).
After increasing size, the plane still intersects at some points, so a Solidify modifier after the Cloth modifier with an offset of 1 (not -1) fixes it.
This is the problem, where you can see the cloth goes through the model and the vertices are jittery
This is everything exactly the same, but scaled x10, notice the nose protruding near the end
This is the solution, x10 scaling plus solidify
Here's the video with the suggestions that worked. The biggest take away besides these tips, is that you should do your animations without relying on the Cloth modifier, and then add this modifier and tweak it so it looks realistic.
Hopefully this will prevent someone's frustration in the future.