I'm traveling to Neerpelt through Amsterdam (I will arrive at the Airport during a morning this weekend). Can I buy train tickets to Belgium, specifically Neerpelt, there?
Could I even pre-order them online, or is that not possible?
Buying on the day you can run into extra costs. There are tickets available to some places in Belgium and I can not check whether Neerpelt is one of them.
If you do not manage to get your tickets online and you can not get them all the way to Neerpelt, you can buy your ticket to the city in Belgium where you have to change trains and buy the rest from a ticket machine there.
Looking at Google Maps I see that combining train and buses (cross border) can be one hour faster than the train. Within the Netherlands you can use the 9292 site, in Belgium 'De Lijn' should be helpful.
In a comment the Trainline is mentioned, I am not familiar with this version, but if it does buses as well, it might be great.