do your weights first nixy, you'll burn energy doing that and then when you go to high energy stuff you will burn fat alot quicker as you've already burnt all your energy.
You need carbs regardless of what people say. No carbs is bad for you.
You need a balanced diet with a decent amount of all carbs, acids, protein, fibre, sugars.. Good carbs come from fruit etc but you just need to be careful with your sugar intake. Watch how much saturates you're eating as those are the bad fats