Cheap inverters are square wave / quasi-square wave. Avoid them at all costs for PC/sensitive equipment unless u have a PC power supply that is able to cope with higher input harmonic content. i.e. HUGE capacitors on the input filter. These inverters produce a square wave output where the RMS is about the same as the wall socket voltage, but it is VERY noisy. OK for apps like lighting, heating, running motors etc.
Sine wave inverters are the best. They utilize sinusoidal PWM to produce a CLEAN sinewave which is representative of that found in the mains wall socket. The circuitry is a lot more complex than the square wave, but they don't produce any "hum" or "noise" when connected to sensitive equipment like hifi's, PC's, medical equipment etc.
Bottom line ... get the sine wave .... its less likely to mess up your equipment.
One more thing ... be wary of the various power ratings for inverters. The one to trust when sizing an inverter is the RMS/Continuous rating.