When working out what size fuse to use with your inverter a good way to work this out is as the example below.....

For a 3000 watt 12 volt inverter:
3000 divided by 10 = 300. So the size fuse you would require for a 12 volt 300 watt inverter is a 300 amp Mega Fuse.

For a 3000 watt Inverter 24 volt:
3000 divide by 20 = 150. The size fuse you would require for a 24 volt 3000 watt inverter is a 150 amp Mega Fuse.

The most common used fuse to use would be a Mega Fuse.

The fuse should be sized from the surge rating of the inverter e.g. Sinergex Pure Sine 3000 watt 12 volt has a surge of 6000 watts that would mean for a 6000 watt inverter 12 volt: 6000 divide by 10 = 600. So the size fuse you would require for a 12 volt 3000 watt inverter is a 600 amp Mega Fuse.
 

Charging a Battery through a 3 or more stage switch mode charger from an inverter or generator

As an example.....

The Ctek7000 7 amp battery charger needs a minimum of a 150 watt pure sine wave inverter or generator. How that was worked out is below:

The scale for 12 volt:
7 amp Charger x 15 volt x 1.2 efficiency = 126 watts
So it works out that you would require an inverter of 126 watts and above.

The scale for 24 volt:
7 amp Charger x 30 volt x 1.5 efficiency = 315 watts
So for 24 volt you will require anything from 252 watts and above.

When working with an older style transformer based charger (heavy) you would change the efficiency to 2 instead of 1.5 or 1.2 which the more modern switch mode chargers use.
For example: 7 amp Arlec Charger x 15 volt x 2 efficiency = 210 watts