Question regarding cloth modifier & animation

Hello! I am new to blender and for a unity project try to make a simple player character. I made him some rudimentary clothes yesterday and then tried to attach a cloth modifier to them - However, when I bake it the outfit kind of 'blows up' and I dont know why it changes its shape like that (I added a picture).

Also, when I animate the character, now the outfit no longer moves with him, but it does when I remove the cloth modifier... Is the armature modifier not valid anymore? I kind of assumed the physics properties of the cloth would let the cloth move with the body (which has a collider modifier)

I hope you don't mind me asking big noob questions here... Have a nice day!