What size of inverter would you suggest if I only want to run the refrigerator and a TV?

I agree with a 200o watt one. The smaller ones seem to be much less robust. I have experimented with several in my F150. The factory 400 Watt one is just about useless. It is amazing how well it is designed and installed but far too weak to power most of my stuff and it is not a pure sine wave one.

You need to install it as close to your batteries as possible. Installing it in an adjacent area clear of the battery air flow would be best for safety. A battery monitor is a really useful tool. I have two blue tooth devices, one for my F150 and one for my lawn tractor. I can check their status in seconds. You don't want to hammer a lead acid battery by running it down too far and too many times, even if they are deep cycle. A 2000 watt inverter won't work as hard as a 800 watt inverter basically and so should provide a much better margin of operation.