Wiring different CREE LEDs together
The most important thing in powering LEDs is to keep the V/A under limits, otherwise they'll easily burn. That's why it's not advisable to use conventional power sources  for them. When the voltage rises, an LED resistance will drop, so there needs to be a mechanism to limit the current in such instances that is not present in those sources.

An LED driver is specially made to fit those requirements. For the power you mentioned, you could buy the finished device at eBay, make a search for "power LED driver".

If you want to build your own, start searching a component supplier like Digi-key for a suitable driver; take a look at its datasheet, usually it has sample schematics for applications.

If you want to power the LEDs from the AC outlet, consider that usually those drivers work at DC and lower voltages, so you'll also need to make (or use) an AC-DC converter. For those specs you mentioned, I'd say it's recommended to use a switching power supply, which is another entire topic.

Even then, I'd advise to build an independent supply (power source+driver) for each set of LEDs (in fact, for the LEDs the better is to have one driver for each of them). Consider that you'll have 4x0.7+1+0.5=4.3A - that's a somewhat high current, but OK. Now, 9x4.3=38A - that's a lot. Not only it's much more difficult to make that, also is more dangerous to handle, and more expensive. And if that one is somehow damaged, all is lost - possibly including the LEDs themselves.