use a 5 V, 2 A power supply to the arduino and then use the Vin and GND pin to supply the LED strip
Yes this way you will have the leftover current @ 5v from a 5v 2amp wallwart in VIN ,leftover current because very small value in mA's is utilised by the Arduino itself which consumption becomes somewhat high as the Voltage regulator's are there.
BUT I don't remember the track traces width over the UNO Arduino that whether it can handle 1.5 amps @ 5v of load.
Step 3 will also work and is essentially the same!
Never Step2 because the output of the voltage regulators will be at complete saturation point @ 1.5 amp need.