LP to residential fridge swap questions

[SHWHLR]

I have a nice 1200w Tripp Lite inverter that I use for the entertainment system. It should be enough to run a 2.6amp/312w fridge and my LED TV etc. I'm unsure if I need to buy an inverter with a built in transfer switch or just add
a transfer switch. When I wired up the inverter I ran the A/C power to the entertainment breaker. I'm a little unsure what the best method is at this point and just exactly how to wire it. Any help is greatly appreciated!!