I had a 1500 watt inverter from Northern Hydraulics that went "poof" the first time I hooked it to the battery. I had a back-up 750 watt I purchased from Home Depot that carried the day for the five days we were without power on October.
The 750 watt wasn't enough to power the refrigerator or the boiler, but it ran the circulator on my wood boiler and charged the rechargeable batteries for the flashlights. As for the refrigerator, there was plenty of snow to take care of the foods that needed to be kept cold.
Remember that your inverter is converting 12 volts into 120 volts, so if you need 10 amps at 120V to run a piece of equipment, your battery and alternator will have to put out 100 (plus) amps. The battery will take care of the starting surge, but prolonged operation will require a heavy duty alternator.
Best regards - Al