Which Arduinoboard is going to be sufficient for my project
Anything will do.
However you will need external hardware if you are going to control LEDs that take more than 20mA.
Power LEDs are difficult to drive correctly if you are a beginner with no experience in electronic design. It is best to get one of the pre built power LED modules like this one:-
http://neuroelec.com/hp-rgb-led-shield/
Although there are lots of others available if you google.