Cutting MDF
While you didn't say what kind of saw that it was, I am assuming something handheld like a circular saw. If so, either the use of the saw or the router along with some sort of straight edge to guide your cut will give you a good cut. I personnaly like to use a circular saw to rough it in than use the router / straight edge to clean it up and do a finish cut so to speak. If using only the router and not rough cutting the stuff first, use multiple cuts (3-4) and make each cut deeper until you ar through the material. Use a good square to ensure your crosscuts and rips are truly at 90 degrees.
If you have not already purchased the material, several of the big box stores (Lowes, Home Depot etc) will cut pieces for you when you buy it. I am not sure how accurate they will be, but even if they do the roughing for you, it may help. If I remember right, cost is minimal.
Another option is to find a local cabinet shop and have them cut it for you on their equipment.
As for the jig saw (the item you provided a link to), I have not had very good luck making perfect cuts with these. The blades tend to flex and wander to much. Again it could be used to rough something in, but probably not for a finish cut.
Take your time, use sharp tooling (carbide), and as always....measure twice and cut once.
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