To lose weight should I be more concerned with fat grams, calories, or carb intake?

Calories. To lose weight, the fat, sugar, carbs, etc are all important but if you decrease calories you normally decrease everything else. Eat 500cal/day less to lose one pound per week. Eating more veggies/fruits, lean protein, & whole grains will help decrease the bad fats & sugar intake, improve the nutrients received in food and still help you lose weight.