There are a few things that I recommend taking care of when you move in. 
 

1. Emergency Shut Off - Make sure you and all family members know where these shut off valves are, in case of an emergency:
-Natural Gas Shut Off
-Water Shut Off
-Electrical Main Circuit Breaker
2. Kitchen and Bathroom Tile - If you have a ceramic tile back splash and or tile in your bathroom, make sure the grout has been sealed.
3. Sump Pump Battery Backup and Alarm - I can tell you from experience that this can be quite costly. The small investment of the backup and alarm are well worth preventing water damage in your basement. This is also a good time to make sure your downspout splash blocks are directing rain water away from your house.
4. Deck - Pressure washing and sealing your deck can help protect the wood from sunlight and water. This should be repeated every year or two, depending on the type of sealant you use and the manufacturer's recommendations.
5. Floors - It is important to make sure that hardwood and ceramic tile floors are protected. Checking the furniture protectors under your furniture can prevent your floors being damaged.
6. Gutters - Check to make sure gutters are not clogged or filled with debris. Gutter guards can help prevent this from becoming an issue in the future.
7. Safety - Make sure your smoke and carbon monoxide detectors are working properly.