I am looking for LED strips and I am asking some questions to myself.
Are you the right person to be answering them?
So, if I understand clearly, I need the strip (that's an evidence), the Mega board (also an evidence) and some power.
AdaFruit is a good company. If they say that a Mega is a better choice, I'd trust them.
In the product description, it is mentioned that the strip works with a DC 5V/10amps.
The picture also shows a second power supply for the Arduino.
Just for my curiosity, if I want for example 3 x 4m of this LED strips controlled by a same Arduino board, could it be possible ?
The implication from the AdaFruit page is that each pixel takes 3 bytes of memory. So, 60 LEDs per meter times 12 meters times 3 bytes per pixel looks like about...2,160 bytes. That's just over 1/4 of the Mega's memory, and needs only 3 pins. So, yes, you should be able to handle 12 meters of LEDs.