To dream of a new house suggests taking on a new character and honing new strengths. It projects your attempt to react in an emotionally mature manner.
To dream of new shoes implies overconfidence in your achievements. This may also mean threading a new path in life.
To dream of being in a new school hints of a notion that you do not belong to the new environment. It likewise expresses the desire to fit in.
In summary, dreaming of new things and places is a representation of new things and situations in your life. You might be attempting to learn and evaluate lessons from previous experiences.