There are any number of products that could be used as cleaners. The thing to remember is that various paint formulas react differently with the various active ingredients in those cleaners. Do your homework, whether that means online research or testing out the combinations, yourself. Shouldn't take too long to find something you're happy enough using.
Alcohol, for example, is warned against when using Vallejo paints, as it turns them into a goopy mess. Other acrylic paints, though, it easily dissolves and flushes away. The fact that most paint brands also sell their own branded cleaner isn't
just an attempt to make money by adding another product to their line - each one is formulated specifically to work with their paints. You don't need to buy a specific cleaner for each and every paint you use, of course, but if you find one to be tricky, the cleaner designed for it is a good place to start.
Windex is, as you've heard, a bit contentious. The primary issue is the inclusion of ammonia, which presents two separate problems: First, breathing in a ton of ammonia is bad. Second, ammonia will strip chrome plating, which is used over brass in many airbrush bodies. Both present very real dangers to you and your equipment...
in a worst case scenario. A little common sense and proper ventilation (even an open window and a spray jar) mitigates or completely erases the first issue. The second is only risky if you soak the parts in ammonia
for a long time. The president of Badger addressed this exact issue, directly, promising that a short soak or flush through the barrel won't hurt the finish, in the least. Spray through a bit of water or another, milder cleaner to clear out any lingering ammonia after using Windex and you're golden.
I've used Windex (with ammonia), isopropyl alcohol (drug store rubbing alcohol, both 70% and 90%), pure EtOH (laboratory-use quality ethanol), windshield washer/wiper fluid (summer formula - not trying to melt ice out of my color cup

), and Vallejo's airbrush cleaner, all to clean several types of acrylic paints and finishes. My findings? All of them work well enough, but none of them are 'magic instant cleaners.' If you can't find an incredibly effective cleaner, just get whatever is cheapest and still works, factoring in your personal comfort level with any inherent safety concerns. For me, that means using the Vallejo cleaner until my test bottle runs out, then going back to using a local grocery store's house brand of window cleaner. I used windshield fluid before that, but kept draining my supply when the car ran low!