Wiring an RGB led light array
Ideally, you should have a current source for each color so you can control their intensity separately. Be aware that a 6 A (6000 mA) current source is not that easy to build and, more importantly, you need to make sure the battery you are planning on using can provide that much current (it should say on its datasheet).

Just to clarify a bit, different colors of LEDs will intrinsically have different forward voltage drop, like you mentioned, and they will emit different amount of light for the same amount of current you put through them. That is why it is very important to have control over each channel (color); then you can fine tune how much of each color you want and likely optimize the growth of your plants.

If you want to have your plant exposed to it for long periods of time, you better consider using a power supply instead of batteries to power your LEDs.

Finally, the common cathode or anode issue will depend on what kind of driver you will use. Some of the RGB LED controllers out there will work with common anode and some with common cathode. My suggestion is for you to decide on how you will drive these LEDs first, and then choose the type of LEDs you want.