Hi David,
I have an Aztec A470, an Iwata Eclipse, and a cheap airbrush from Harbor Freight. I learned on the Aztec and continued to use it after buying the Eclipse. Unfortunately, it broke about a year ago and I never sent for a replacement.

The best cleaner for your airbrush really depends on what you spray. In almost all cases, the thinner for a given line of paint works best for airbrush cleanup. Windex works well with Tamiya acrylics. Lacquer thinner will cut anything but requires special handling.
Acrylics tend to dry faster than enamels or lacquers and thus clog tips more easily. Properly thinned paint helps delay this process. Hot, dry weather accelerates it. You can retard the drying time of some acrylics by adding dish soap. Liquitex sells a product called Slo Dri that does the same thing. However, not all retarding agents work well with all acrylic paints, and too much retardant can cause unwanted results. Again, you have to experiment a little.
Enamels and lacquers are easier because they stay "wet" longer. Most enamel and lacquer paint lines have a dedicated thinner that performs very well for thinning and cleaning.
You can help prevent clogging by blowing some thinner through the tip after each color. Do the same thing if you need to put the airbrush down for a while or the tip starts to sputter. The cool thing about the A470 is that you can dismount the color cup at any time, mount another cup with some thinner, blow it through, then switch back to the color cup. Increasing air pressure will sometimes blow out a clog. As a last resort, you can drop a clogged tip in a jar of thinner, wait a while, then fish it out and blow some thinner through it.
Good cleaning will really help prevent clogging. After you finish spraying, blow thinner through the tip until it comes out clean. Unscrew the tip and wipe off any remaining paint. Problem tips can be stored in a jar of thinner, but I rarely found this necessary. Now look down the nose of the airbrush. If you see any paint down there clean it out with some cotton swaps or whatever. Try not to leave behind any lint. This is critical--paint will accumulate down the little side tunnel on the opposite side where you mount the color cup. If you are right handed, this will be on the left side of the brush. There is a little pin closing off this passage. Pull it out and clean the passages on _both_ sides. A little piece of paper towel (or whatever) wrapped around a toothpick should do the job. Put the pin back when you are done. Be careful when cleaning down in there. The A470 is fully enclosed but you can still damage the pin that pushes against the back of the tip.
I begin every session by blowing a cup of thinner though the tip.
One last thing--all airbrushes tend to gum up when spraying multiple paint types in the same session (i.e., acrylic then enamel). I found the A470 particularly vulnerable to this problem. Clean well after each paint type. Even better, clean up and switch tips, too. Remember that little side passage--it's a natural paint trap.
Please consider all of the above guidelines, not rules. Practice and experiment until you find what works for you. Also remember you can paint more than models! Toys, trinkets, and junk around the garage all make for good test subjects. One time I painted all the vent covers in the house.
Good luck and if you have more questions come back and ask.

There are lots of great modelers here who can help.
-Doug