I've built a few hydro/aero systems, and the only aspect that's really important to get a good growth rate is keeping the roots oxygenated.
My favorite is aeroponic, where to roots are just sprayed with water every 15 minutes. Great growth rate, but if your pumps fail, the plants die within an hour.
Bubblers works the same way as aeroponic, except that the roots are in clay balls and only bubble film touches the roots. Same problem with pump failure.
Ebb and flow is also great, the roots alternate between absolute submersion and recession, and can be rigged so that pump failure results in long-term submersion instead of drought, giving you a couple days to find and fix the issue.
Standard hydro keeps the plants submerged constantly, and introduces air bubbles into the water. This is by far the safest and easiest to build, but requires regularly cleaning air stones and doesn't have as good of a growth rate as any of the above. Running two sets of air pumps and stones is a simple redundancy and even increases efficacy.
All of these methods only require a container (or two, for ebb and flow) and either a water or air pump on timers.