What Arduino to chose?

You should also get some transistors for driving more LEDs. Then you can use a higher supply voltage (12V, 15V) and have longer columns of LEDs in series turn on with one control pin.

Here's an example where I had a 12V supply & used it to drive 20 LEDs. One arduino pin turned on the transistor to turn on the 20 LEDs.
2 other arduino pins turned on 2 other transistors to turn on 2 other sets of LEDs.
I needed 5V for the LEDs, so I used a 7805 to regulate the 12V down to 5V.

I also used the left hand transistor to invert a data signal that I needed to go to the arduino (vs using a logic chip).