Keep logic signal cables as short as possible, decouple the supply a lot, decouple the devices that switch the LEDs even more (LEDs switch fast, fast switching causes havoc, fast switching many amps is bound to cause issues).
I'd suggest 470uF electrolytic and several 220nF ceramic across the LED supply right next to the switching device.
The motors may need decoupling to suppress inductive spikes.
Use twisted pair cables for all heavy current loads, don't run high current cables anywhere near logic wiring.
Make sure the grounds for all the supplies only connect at one point and that that point doesn't carry any heavy currents. This point is ideally at the Arduino.