Typical is what the inverter has to supply on a steady basis. This is usually much lower than the surge. For example, this would be what a refrigerator pulls after the first few seconds it takes for the motor to start up, or what it takes to run the microwave - or what all loads combined will total up to. Average power would usually be much less than typical or surge, and is not usually a factor in choosing an inverter. If you run a pump for 20 minutes and a small TV for 20 minutes during a one hour period, the average might be only 300 watts, even though the pump requires 2000.
Average power is only useful in estimating battery capacity needed.
Inverters come in size ratings all the way from 50 watts up to 50,000 watts, although units larger than 11,000 watts are very seldom used in household or other PV systems. The first thing you have to know about your inverter is what will be the maximum surge, and for how long. All inverters have a continuous rating and a surge rating. The surge rating is usually specified at so many watts for so many seconds. This means that the inverter will handle an overload of that many watts for a short period of time.