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

What type and size of battery do you have?

Add up the peak continuous wattage of the refrigerator and TV, add some extra (maybe 25%) safety margin, and that would be how much you "need" in the current situation.

More is probably better for unplanned changes. But your battery system will set an upper limit to how much it can deliver.