The inverter's ratings are usually roughly close, I've not heard of too many complaints unlike what you hear about generators!
You have to choose something that will handle the peak load continuously without overheating. My fridge draws 380W on 240V so I'm using a 600W inverter. It happens that Aldi flog these inverters for about $59 and they're electrically isolated - so they're perfect. Powertech (Jaycar, Rays Outdoors, BCF) is also a good choice, the entire range is electrically isolated.
Be mindful of the amps that an inverter will draw. They're usually around 85-90% efficient and for a little 150W unit you'd just shrug and let it be. However, if you've got a 1500W/3000W inverter that's 85% efficient (and will supply 3000W peak) then its peak amperage drawn from the battery will be (3000/0.85)/12 = 294 amps. I recommend something a little better than leftover speaker wire for that!