Mewtwo's neutral isn't the best neutral he can't do much in it, he can only really shadow ball. Some of his Bread and Butter combos are U-Air Strings in hover. His movement is the best part about him, he has arguable the best recovery in the game but for his movement practice sweet-spotting ledge with teleport, but his movements are Hover and Teleport, They are both extremely good but you must know when you should use them. Teleport is a great approach tool, teleport into fair or bair. Tomaster has the matchups down. Practice movement and using teleport to the fullest. Try to learn how to do hovercancelling after movement.
Have fun with my tips