Rather than buy individual train tickets for each of our day trips, it would make more financial sense to invest in passes. Can anyone tell me what kind of pass I should be shopping for?
Your quoted statement is not always correct. It is true that waiting in line every day at the ticket window can be tedious, and even cause you to miss a train. But many of your trips are likely to be very short distances, that are "a waste" of a day on a pass. Also, you have two entirely different countries, with two entirely different transit systems. You also have to consider that many historic town centers are not "at" the train station, and you may need a bus or a tram to make the best use of time on a daytrip. (Sometimes, like in Antwerp, the walk can be worthwhile, as long as you have enough energy. In the case of Belgium, it's important that Brussels has its own bus/tram tickets and multi-trip cards. The other cities in the same area have a unified transit system where you can use the same bus/tram card in multiple cities.
I will say that I have bought some 10-trip tickets that can be shared at will in Belgium. But they are not always cheaper than individual trips. But if there is a line at the ticket window, they can be handy. I always write in a station farther away (before departure, as required) on the same line, in case it starts to rain or I read in my travel book about a closer worthwhile stop. You need to look into buying a physical Netherlands card that may speed tickets for both trains and transit, I'm not an expert on that one. Used to be hard for non-citizens to get, but I believe it's easy today.
Some posters here have reported success at rail ticket machines (i.e. shorter lines), others, even those with Chip and PIN cards, have had difficulties buying single, current-day journies at a machine. AFAIR, Belgium does not let you buy simple tickets for local journies on future days, to save waiting in line. The tickets are good "today only."