Watch out as well for the cheaper inverters that claim a certain power rating but fail to deliver it for a number of reasons.
I bought one from a Chinese Ebay supplier that claimed '3000W / 6000W peak' but in practise it only seems to be able to reliably cope with much less. Connecting a 2400W kettle causes it to go into instant overload protection. I only use it to run the LED lighting in my caravan now. I resorted to a diesel generator for the kettle etc.
I understand many types of load classed as 'inductive' (some motors, fluorescent tube ballasts etc) take a much higher current than normal for a few seconds on start-up, such that you might need an inverter with a rating much, much higher than the appliance's normal constant running rating in order to get it started reliably.
I might be wrong but I think there's a technology called 'soft start' on some inverters that tries to cope with inductive loads by slowly ramping up the output on load connection, so there isn't so bad of a sudden current rush