Paintings will do better over time when they are displayed and stored in rooms in your home with less differentiation in the heat, cold and humidity. Living rooms, bedrooms, living rooms, etc. are better. Bathrooms, kitchens, attics and basements would be the worst!
List the most important items to you. Taking extra care with your most valued possessions will help you feel less stress during the moving process. It is an exciting time, after all, and can also be an enjoyable experience!