It all depends on what you intend to do with your system.
For myself personally I hate the sound of a water pump, so it is all air cooling for me (though some new pumps are pretty quiet so I may have to revisit my opinions on that in the next year or so). As I am rather picky about sound I have low RPM fans on everything, and even an aftermarket GPU cooler to keep things quiet (and it also happens to keep things cool as a nice afterthought even though I don't OC the system much anymore).
The thing to remember here is that a stock cooler is only good for stock settings. If you want to do any overclocking, or if the stock fan is too loud, then an aftermarket cooler is an absolute necessity.
Water coolers are pretty neat, easy to install, keep temperatures very low, and are quieter than most air coolers (though the quality of what little noise they make is a bit more grating than a normal fan... at least to me), but just keep in mind that you get what you pay for. A cheap water cooler is going to be no more effective or quieter than a cheap air cooler. Keep in mind also that your case may need to support water coolers with enough space in specific areas to accommodate the thick radiators and routing for the tubes. Most cases can fit a 120mm water cooler just fine, but bigger radiators may have more requirements, so do your research ahead of time.
Air cooling is much simpler, but also has some requirements. The ever popular CM 212 EVO or Plus are great coolers (I use a modified EVO myself) and are dirt cheap. But because they are cheap they do not come with the quietest of fans, though they are plenty effective at cutting the heat down. Thankfully the EVO comes with a 2nd set of brackets to add a 2nd fan, and the stock fan is very easy to replace. This allows you to buy 2 high performance fans for much better cooling, or (like in my case) 2 quiet fans for extremely quiet operation with much better cooling than is provided by stock coolers. The only potential issue is height clearance between the motherboard and the side panel of the case, so make sure your case can fit it (most can just fine). There are other more expensive coolers on the market, but they are essentially the same 212 cooler with better quality fans, so why not just get a 212 and put even better fans on it for roughly the same price?
If you want a more exotic air cooler than spend a little extra on a Noctua cooler. They are not exactly pretty, but they are dead quiet and extreme performers, and not nearly as overpriced as they use to be. Just be aware that these are very heavy coolers, and cheap motherboards may not accommodate the added weight very well, but most gaming boards should do just fine.
If you do not overclock, or are fine with the sound produced by your stock cooler then there is no need for either a water cooler or an aftermarket heatsink.