Arduino integration with LED lamp

Hi to everybody!
I'm a beginner in Arduino, with some experience in programming.
I'm preparing my thesis project, and it's about integrating arduino in a led lamp.
I explain.
I want to connect to arduino
-a rotary softpot for controlling the rgb of the lamp
-a potentiometer for intensity
-a small microphone for controlling the on/off switch by clapping (for example).
All these signals are send by an IR to the led (GU10 model).
The idea is to place Arduino in a small base, that is also a lamp support.
In addition, I need arduino powered by batteries.

I want to ask you, what Arduino model could fit better in my project, without losing any of the functions i wrote before. Basically I need the smallest Arduino doing all of these things.
Can you help me finding it out?

Thank you in advance.