Amsterdam to Bruge in early August

I found the countryside between cities nothing special but why not take your time and stop off at Leiden and Delft
on your way to Brugge

That route goes through the most densily populated area of the country. There are some stretches of nice countryside between Haarlem and The Hague, but it doesn't add up very much.
A better route is from Amsterdam to Roosendaal via Den Bosch (officially 's-Hertogenbosch). It has three major river crossings and till Den Bosch goes through relatively empty countryside. Choose the »More options« box on the NS rail planner for the schedule.

Tonfromleiden, thank you for the suggestion. I think that I will travel per your plan. When I look that itinerary up on the Dutch rail site, it says that the fare is not available. Can you tell me why that would be? We are going to be traveling out of the Amsterdam Bijlmer Arena Station, south through Utrecht. Will we be required to buy the ticket at the station, or can I pre-purchase it online? It's sometimes fun to figure things out, and sometime really helpful to have an expert explain things. This is one area where i could use some help. Thanks in advance.

You're right: »Prijs onbekend« as they tell me in Dutch. Probably because it isn't the shortest route: 16 mins longer than via Rotterdam. Just buy a regular ticket for EUR 20,50. In case the ticket collector shows up, explain you thought via Den Bosch was the easiest route. You're after all an ignorant foreigner, aren't you?
I don't think you're able to buy that ticket online. NS only accepts payment with iDeal: a perfect system, but only available for holders of a Dutch bank account.

Would I just buy the ticket from an ticket vending machine at the station then? I wasn't sure if I could get on any train at any time, going any direction with one of those tickets - the website doesn't explain it to me well enough. I'm traveling with my family of 5, and I like to be prepared, so there is less confusion and stress, especially when trying to travel to our next destination. Do you know, is there a "day ticket" for a family available?

I have no personal experience with travelling with a family. A group ticket doesn't seem the most economical way at EUR 55. Children 11 yrs or younger can travel on a Railrunner for EUR 2,50, and children 3 yrs or younger have free travelling. This page gives the necessary information.
Tickets are valid on all trains on the day of purchase.
I travel on an OV Chipkaart, so I wouldn't know how you can get those tickets from a machine. I would feel more comfortable to buy those tickets at a window.