What are the factors that make the membrane more permeable to Potassium ions than Sodium or Chloride (or any other ions)?

The two-pore-domain potassium channels. There is otherwise nothing intrinsic in the membrane that makes it more permeable to potassium, but the membrane contains these channels which are referred to as "leak" channels because they are not voltage-gated and are always open. These allow cells to turn the concentration gradient maintained by the sodium-potassium ATPase into an electrical gradient.

Other channels are also present and can contribute to the membrane potential at rest, but the two-pore potassium channels are typically the largest contributors.

Most of what you've written as background in your question is only applicable to rest so be sure to consider that as you learn about action potentials and post-synaptic potentials. What is true is that if you were to hold a cell at 0 mV without any voltage-gated channels, you would see much more potassium leaking out than other positive ions moving in, and this is why the inside becomes more negative (establishing the resting membrane potential). The resting potential is the potential at which the net charge of ions flowing across the membrane is equal: that is, there are just as many positive ions flowing out at rest as there are flowing in. If anything else were true the cell would not be at equilibrium and the membrane voltage would continue to change until it were true.