Get yourself a 5V power supply capable of powering all the LEDs, and another 500mA for the Arduino.
Tri-color LEDs can draw up to 60mA/package when running full bright on all 3 colors.
144 x 0.06A = 8.64A
A 5V, 10A power supply would be sufficient. >=10A is fine.
Power the Arduino either thru its USB connector, or via the 5V pin on the power header.
Both the LED strip Gnd and the Arduino Gnd must connect to the power supply Gnd.
Example: 60 Watt Power Supplies | MPJA.COM
You can also connect the 5V supply & Gnd just to the strip, with the strips data & Gnd connected to the Arduino.
Then connect the Arduino to your PC for downloading code and powering just the Arduino.
The key to correct operation is that all Gnds be connected together (Arduino, LED strip, power supply). The 5V supplies do not (strip has one, Arduino can have its own; when you do not need the PC anymore, then USB power can be replaced with the 5V supply power).