Clean, tightly closed containers are the best defense against spills and wayward odors. Sealing out air also keeps food fresher longer. And if any spoilage does occur, it'll be limited to the unfortunate food in question.
If you do need to repackage, opt for clear containers if possible. If you reuse containers from store-bought food, label them.
Finally, don't let your efforts be in vain: Remember to plug in the fridge and turn the temperature control to "on." Choose the lowest setting until the compartment is good and cold -- 38 degrees Fahrenheit (3.3 degrees Celsius) or a hair under -- before returning the occupants to their gleaming abode.