the basics are always best....
I commute long distance with my SHOs, and make it a point to check the engine while fueling up.
For a quick check on an unknown car before a long road trip, I would:
1. check the air filter - new!
2. check (at least) or ideally change the oil - the guy i got the car from swapped the engine over so the oil is new.
3. visually inspect the plugs and lines (as much as you can), feel the rear ones - new plugs!
4. look to see that all of the vacuum hoses are intact
5. check the battery cables and clean them - they're new too!
6. rev the motor with the hood open and listen for any funky noises
7. for the suspension, hand-check at least all of the lug nuts
8. downward pressure on each wheel to get the status of the suspension
9. side-to-side push pressure at front and rear for the same
10. do a hard-brake check at slow speed to ensure that the brakes are functioning under a hard stop
11. work the transmission through all of the gears and make sure it is shifting smoothly
12. work the steering through a few hard pulls to see how tight it is.
This is a basic list but should unmask any major problems that are likely to come up on a long trip.
Best of luck,
JD