Essential medications to have at home for a baby include Vitamin D drops (especially for breastfed babies), Tylenol/Advil drops, and Benadryl. Other products to consider are rehydration sachets, gentle skin cleansers, diaper creams, baby wipes, and a nasal aspirator. It's also important to have a thermometer, various bandages, and sterile compresses on hand. Remember to take care of yourself as well, with items like lanolin cream for breastfeeding mothers and a good moisturizer. Congratulations on the upcoming arrival of your baby!