Remember to enjoy yourself! It may not be a ton of fun to have to move but if you stop and attempt to enjoy yourself then it will make the whole process go more smoothly.
While this may seem like just another thing that’s added to your plate, get copies made of all of the keys before you move. In all of the chaos of the move it would be easy to misplace a key, and that is the last thing you want to deal with on your moving day.
If you are looking to save money, you should move during winter. Winter is when rates tend to be the lowest.