So far I have an accelerometer (ADXL335), 2 Voltage regulators and an Arduino uno
An odd mix of things.
I would abandon the accelerometer and use a simple tilt switch. I am not sure what you need two regulators for and the arduino looks like over kill. It is a project you could just do with a 555 timer.
what kind of LED's are most powerful
Bit of a silly question because it is like saying what sort of car is the most powerful, the answer is the powerful ones.
If you are just lighting up a logo from the back or is the logo made of LEDs? White LEDs are brightest for a given voltage and current. If the LED's current is below 20mA then there is no need for any cooling.