Advice Regarding Chaining LED Strips
These strips are composed of multiple parallel segments of three series LEDs plus resistor. When you add multiple strips together they are still in parallels so the voltage does not change. You want a power supply that's exactly what you will already said, 12 volts at 4 amps or higher.

Keep in mind that flexible printed circuits like these LEDs are on have a high resistance so the voltage will drop the farther down the line the LEDs are from the power source. The ones at the end will be less bright. Ideally you would provide power every five meter section, with a parallel connection using regular wires.