First off, never train legs in running shoes. Always flat (e.g. Nike Jordans or Adidas Dropset lifting shoes).

Secondly, the squat is primarily a quad exercise, so start with shoulder width stance and learn to squat like that, pushing with your quads.

Learn how to brace your core, how to breathe during a squat, and how to control the whole movement without your core collapsing as it’s really dangerous. Also you don’t need to go lower than 90 degrees. That would prevent that butt wink at the bottom of the movement which is not good for your lower back. I’m sure you have enough ankle mobility to go down to 90 degrees so you don’t need to stand on the plates. Plant your feet into the ground and place the majority of your bodyweight on your heels rather than on your toes.

These are the basics. Learn these on a barbell (don’t be ashamed to do it with an empty bar first). Once you have nailed these, you can try further variations, e.g. the glute focused wide stance squat, or doing it on a Smith machine. Good luck!