Fat burning fat is a second order effect. Don't base your weightloss strategy on it. You are, afterall, trying to burn a saturate fat - palmitic acid.
Mix it up. Fatty protein, especially on the bone, has some benefits over your alternatives. Don't overthink it. Don't be overly restrictive. Variety is fun.
Don't go very low carb either. Most feel best around 100g per day. Down to 50g if you're trying to lose weight
Four years Primal with influences from Jaminet & Shanahan and a focus on being anti-inflammatory. Using Primal to treat CVD and prevent stents from blocking free of drugs.
Eat creatures nose-to-tail (animal, fowl, fish, crustacea, molluscs), a large variety of vegetables (raw, cooked and fermented, including safe starches), dairy (cheese & yoghurt), occasional fruit, cocoa, turmeric & red wine