300 watts is about 30 amps at the battery 14GA is good for half that at 120 volt and even less at 12 volt due to voltage drop.
Plus there is a voltage drop INTERNAL to the batteries (I do not know how much)
The key to battery/inverter is three fold
One, Keep the leads as short as you can but do not mount the inverter inside the same space as the batteries
Two HEAVY cable for a 300 watt Starter cable works very well and is low cost up to around 750 watts it works well. long about 1000 it might be a bit...er.. anemic
3: for as much of the run tape or wire loom the cables like this ============
Side by side. This is more important on larger inverters.
AND MORE battery never hurts..
DEEP CYCLE batteries work best for House use.
(As opposed to MARINE/deep cycle) note how I use case on those)