A bit more clarification:
Lights can have more than just those two modes.
Some likes are sound active only. These are typically your high-tech FX, such as the Aggressor. They often do not utilize DMX, so they must be turned on/off. This can be done via the usage of a dimmer pack with the channel set to switching. I have several high-tech FX, such as the Mystic, Vertigo, Rover, Electra, Barrel Flex and Reflex, just to name a few.
Some fixtures are DMX only, which means you have to control them via a controller of some sort. Some fixtures also have a sound active mode while under DMX control.
Some fixtures have master/slave modes. This means you can chain some fixures together, and the first one(which also must be indicated as master) will then control the behavior of what the slave fixtures do(ie: follow what the master light is doing).
Some lights are able to utilize more than one of these functions.
Now, lights such as the aggressor have a knob on the back to adjust for sensitivity. If they are acting up too much, just turn that knob down. My Mystic and Vertigo have this feature, while I'm fairly sure my Electra does not.
If you want maximum bang for the buck, then you save money by saying "screw DMX" and going with all high-tech FX. I'm not saying you can't do a good stage show with it, because one can. What you do have to realize is you give up pretty much all control. You will need to buy some sort of turning on/off system, such as the ADJ SC-8, which basically gives you remote control over up to 8 sepparate fixtures. As I'm sure you're going to want to change what's going on now and then, this is a cost-effective solution.
But, if you go the DMX route, you can still incorporate high-tech FX into the mix. But now you have to buy some sort of controller, and then to go with that, dimmer packs. Your cost rises considerably now.
I'm not saying which way to go. If you invest wisely, then you'll have minimal waste. If you go with the SC-8 and later go onto DMX, you retire your SC-8 since it's not needed anymore. If you go DMX from the get-go, your investment jumps up because of the necessity of buying dimmer packs and a controller.
UNLESS: If you go all DMX capable lights, you don't need dimmer packs but you still need a DMX controller of sorts.
Regardless of which way you go, I recommend lights that are going to cover a large area. The Mystic can handle that task as well, and maybe going back and forth between the Aggressor and the Mystic might be fun. And to sort of break things up more, maybe some sort of scanner-type fixture such as an Electra or Reflex(or 2)
You're diving in deep. That's how it goes starting out. Don't forget you have to mount the lights somehow, either via T-stands or trussing. ADJ has some very affordable solutions.