1 amp Ac equals ~10 amps Dc
If by chance you can get a DC plug adapter for all your devices then you may not need an inverter, since the inverter will use some power this will make the battery last longer,
You only want to drain your battery by half or less, which means if you have a 100ah battery then you only want to use 50ah before you charge it up again, the more drain you do past 50% the quicker you will age your battery.
AGM batteries charge differently than normal wet lead acid batteries, make sure you get a charge controller that has settings for an AGM, will increase the lifespan and usefulness of the battery.
my bus thread, http://www.skoolie.net/forums/showthread.php?t=8860&highlight=bubb