Bryan,
I've got 9 Propar 56s and like them very much. They are perfect for the spot lighting of my six member band. But the lights are all about 10' away from the performers and I can control the other lights in the room (with which they compete). I can't say they would be great for you because I have no idea what your situation will be like.
The problem is how much light you need to make an impact will vary depending on how much other light (call it ambient light) is in the gym, how far away the lights are from the thing you are trying to light, and the color of the the things you are trying to light.
For example, if you tried to use 4 Par 64s outdoors in full daylight to light up a black funk band wearing black clothing, it is unlikely that anyone could tell whether the lights were on or off. If you used them to light a white rock band wearing silver spangles in a room that otherwise had no lights but the exit signs, they would be amazingingly bright and effective.
My guess is that if your trusses in the gym are 10' - 15' away from your performers/subjects, there is little other lighting in the room, and your performers are about average in skin color and clothing, four Par 64s will do a fine job. The more your situation departs from that situation, the more or more powerful lights you will need.
I wish I could be more specific, but this is the reality with which you are dealing.
Using two or more lights to light your subject is better than one. One light tends to cause unflatering shadows on faces (below the nose, for example). But when you try to use more than one light, the multiple lights are usually farther away from the subject than one directed light. The intensity of the light fades exponetially the farther way from the subject. So the more coverage you try to achieve with a light, the less effective it will be. Consequently, it usually takes more than twice the number of light to achieve the same intensity as one light close and directed.
If your gym has windows that let in outdoor light, your results will vary depending on whether it is light or dark outside and the time of year. My guess is that there will be no substitute for trial and error.
Any controller will allow you to do what you described. The cheap controller, however, will require that you do everything manually every time you want to change the light settings. More expensive controllers will let you record different "Scenes" or "Shows" that will enable you to quickly and easily change from one situation to another by hitting a button.
Hope this is informative, even if not acutally helpful.