Not trying to negate the usefullness of the forum, but this is an often discussed (debating, and argued) topic on the Corvette and Miata forums, you might look over there for some of the age old threads for more info
"WAX" is a pretty generic term anymore it seems, and doesn't necessarily imply the product is any kind of wax at all. A wax these days can be a polish, or kind of surface protection other than wax-based.
If you're dealing with a new or custom paint finish I would stay away from cleaner-waxes. The cleaner-waxes commonly "clean" by adding an abraisive to the product. As you "wax" you're also polishing, lifting paint as you do so. If you want to polish, get a polish, if you want to wax get a wax.
Aside from the cleaner-waxes I don't think there are any waxes that can damage your paint, so a lot of trial-and-error can lead to what works best for you. Start with a good reputable brand name and go from there. Mothers and Meguires are the most commonly used brand names out there. Zymol has a reputation for making expensive "custom" waxes (specifically designed for certain model cars) but their consumer walmart products have a poor reputation. Spray-on and liquid waxes can sometimes have a high alcohol content which isn't necessarily desireable, especially if your paint is prone to "streak" when waxed.
One other comment on regular waxes and waxing - a lot of what the final result looks like comes through careful preparation of the vehicle. Just washing a car and waxing may not be enough, especially for a daily-driver car. The paint picks up tons of contaminants, especially when driven often. A good washing, followed by a careful clay-bar procedure will result in a perfectly smooth paint surface free of contaminants. A clay-bar system lifts contaminants embedded in the paint(including metal particals, dirt, etc) without polishing away paint. Sounds like black magic, but the results are incredible. If you've never tried it, try it - a freshly clayed car looks and feels like it was just waxed. A freshly waxed and clayed car is even better.
There are other paint treatments available that are not waxes at all. "Zaino" products have earned a cult-like following and are not a wax at all. Zaino is a multi-step paint application (Zaino calls it a polish, which I don't agree with) that builds up in layers. When properly applied and cared for the Zaino products can result in some of the deepest, slickest, long-lasting shines around. The advantage to Zaino is that it will not slick-off or lift in hot weather (some waxes will), builds up in layers and stays on the car (waxes will evaporate and wash off over time), and is optically pure.
One last comment; no matter what "wax" you choose please choose your applicators and towels carefully. Cheap applicators can scratch paint, only top quality applicators should be used and only 100% cotton towels should be used to wipe the wax off. Sal Zaino's commented that only "100% Cotton made-in-USA" towels should be used. Many foreign-made "100% cotton" materials aren't actually 100% cotton (go figure), and the filler-fibers they use can scratch the paint. I've followed that rule and my MG is pretty much free of any swirl marks or scratches from waxing, even after years of shows and driving.
Finally remember; no matter what recommendations or research leads you to a specific product use what works best for you.