Originally I was just "scratch bashing" planes out of foam before I made a foam cutter, it's messy, but you can literally build the entire plane without any fancy tools at all. I was using my jig saw to cut out the pieces and used a rough file and sandpaper to get it to the general form, then finer sandpaper to get it to it's final form. Hacksaw blades are a popular low tech choice when cutting out pieces and I use my table saw and chop saw for the booms still since they are just simple shapes.

I used Critterhunters bandsaw technique simply by mounting the bow to the side of the table, mainly for the purpose of making a foam flying saucer, but making perfect circles with it, there are some extra steps to do one of those, especially when making a circular symmetrical wing, again, remounting the bow at a few angles around the pivot point, the tool does have major advantages with saving time and to get more precise cuts not to mention as fisher said, addressing the mess factor.