What inverter to get for a Dometic CFx35 fridge

https://www.dometic.com/en-ca/ca/products/food-and-beverage/coolers/electric-coolers/dometic-cf-35-_-140221

12 and 24 volt is DC, while 110 v is AC. Your two batts in series will be 24v if they are 12v batts or else 12v if 6v golf car type (GC2)
Which do you have?

Is this for the starter battery or the house?

Usually, cig plugs are low watts with thin wires and not good for bigger DC loads, which need fatter wires to the battery bank.