400w / 12v = 33.3a, you're going to need a 40a MPPT controller to really utilize that panel.
AGM batteries, being a flavor of lead acid, are only good to about 50% Depth of Discharge (DoD) so that battery is only going to be good for 60Ah at 12v or about 720 Wh. Just to be aware that the inverter is going to have a few watts of draw 24/7 if it's just sitting there idle.
As long as you're aware of the limitations you'll be fine.