I'm gonna go with @Golden_HVAC, and suggest that unless you have at least 4 house batteries, you are not going to be happy with that inverter. The coffee maker alone will drain battery power like crazy, and a 1200 watt inverter is way more than you need for the TV. The inverter itself is going to be a large and very inefficient drain when powering just the TV.
I think I'd lose the coffemaker. Get yourself one that uses propane instead, then size the inverter just for the TV. Then you won't NEED a transfer switch, as when you wanna watch the tube on battery, you switch the plug and turn on the inverter instead of just the TV. That's a LOT less work than wiring up the transfer switch, and cheaper to boot.