We are arriving at 12:30 pm (from Amsterdam) and want to take the train to Cinque Terre. Is it possible to make the 2:00pm train or should we just relax and go for the 4:00pm train? I'm thinking the stars would have to be in alignment to make the 2:00pm.
I think you are a good astrologist.
You would need several stars and planets perfectly aligned to be certain of being aboard a train 1.5 hours after landing, even with Linate being the closest airport to the city center. If your plane were just half hour late, you'd be out of luck.
I assume you're planning to buy an advance ticket for the train to the Cinque Terre?
The easiest solution would be to simply take a shuttle or taxi from Linate to Milano Centrale, and then buy a ticket on the next train heading towards the Cinque Terre. Which of the five towns are you going to? Hopefully you can connect with a train that has minimal changes.
Looking at prices for tomorrow (so, highest fares), the Base fare (undiscounted) from Milano Centrale to Vernazza is €27.10. For that low a price, I don't think it's worth booking a discount ticket that you may not be able to use. I'd do as Ken suggests - just buy a ticket when you get to Milano Centrale for the next train.