Just to keep apples and oranges in their respective boxes, PEAK power is the highest voltage level produced by a sine wave, which is 1.414 times the true or RMS (Root Means Square) power of the wave or, inversely, RMS is .707 the Peak voltage. The Maximum power is the most current (or wattage) that the power supply will draw when it's outputs are loaded to the max. In computers, that's usually the point when power is first turned on, power is applied to the motherboard, processor, and peripherals, and the disk drive(s) start turning. While desktop or tower computers may well need a 200 - 300 watt power supply, most laptops require much less power to operate. That 6.3 amps you mentioned is, in all probability, at 12-15 Volts; or about 64-90 watts.
Next, pure sine wave inverters vs. modified sine wave inverters: Most, repeat most appliances will operate properly using a modified sine wave. My microwave oven does not. Electric blankets with electronic controls do not. Clocks do not. SOME computers do not. There's no way to tell until you try it out. Almost any purely resistive devices like incandescent lamps, toasters, electric heaters will operate fine. Should you opt for a pure sine wave inverter instead? Given the current use of electronic controls and small yet efficient switching power supplies being used in many modern appliances, I would go with the pure sine wave over the modified. However, a like-size pure sine wave inverter - say a 2kW unit, will cost about double that of it's modified sine wave cousin. Because I already have a modified sine wave inverter installed, I can't cost justify replacing it with a new one just for those few things that don't operate properly. I've modified my electric blanket control to be happy with it, and use my generator when I want to use the microwave (assuming I'm not on shore power) If you're doing a new install, then definitely go with a pure sine wave unit. Just my humble opinion; others may not feel the same way.