Upon getting a new car, the main things to check should be:

1. The signals.

2. Lights - Headlights, high beam.

3. Audio system/Radio.

4. Bonnet, boot, petrol cap.

5. Wipers.

6. Airconditioner.

7. Rear & side mirror adjustments.

8. Seat adjustment.

Check out this video if you've just gotten a car and doing some initial checks and adjustment!