Standard na ginagawa ko for a long road trip

Tires:
1. Tire pressure
2. Tire nuts
3. spare tire pressure

Engine:
1. Water level
2. Oil level
3. steering power fluid level
4. Water reservoir level
5. brake fluid level
6. washer fluid

Electrical
1. Headlights
2. signal lights,
3. tail lights
4. hazard lights
5. wiper and washer

Trunk
1. spare tire(although this is covered in Tire checking)
2. jack
3. basic tools(pliers, screwdriver)
4. Early Warning Device
5. At least a liter of water(just in case)
6. a small container of brake fluid
7. baggages
Interior
1. Seatbelt
2. seat position
3. some candies (very useful for long drives)
4. cd's(not all should be mellow music lest you want to get sleepy)
5. Map of your destination
6. passengers(if present)
But since your car is new, you may not need to check all of the above but no harm in doing all the checking though...
you might also want to check for hotline of your insurance, or towing service provided by your insurer or dealer.

And also you may want to check the weather(not necessarily from our very reliable PAGASA ), your possible pitstops (rest points).

Have a safe and pleasurable drive....