Lets get back on track here. The op wants to know witch speakers give the less trouble. I will say passive because they are the simplest part.
The next question was amplification. Again I would go with power amps, because they are easy to change and you can get a variety of types of amps, from class A to class D. With powered speakers your stuck with what ever comes with the speaker, witch is generally a class D amp.
The last question was the mixer/controller part, and there are a vast options here as well.
So start with what provides the best signal, the mixer/controller, then work your way down the signal chain to how your going to control that signal. From ther you have the option of going passive or powered speakers. Th simplest being passive because you have more options between what types of xovers, amps you use and the last being the speakers themselves. How long will they last and how easy they are to replace. You can blow up any system no mater what they cost, that comes down to the discretion of the operator. Know what your system is capable of and don't exceed it.
I think suggesting anything above a class D for DJ work could be dangerous especially to someone new to this. Class A are going to sound real sweet but to run 2 speakers on sticks they are very inefficient. You're also looking at some pretty big cash outlay if you want a good class A
I also disagree with passive being better. I prefer passive myself but I run powered most nights simply for weight. I think they both have their upsides and downsides but comparing apples to apples neither is really better than the other